Inflation (cosmology)

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In physical cosmology, cosmic inflation, cosmological inflation, or just inflation is the exponential expansion of space in the early universe. The inflationary epoch lasted from 10⁻³⁶ seconds after the Big Bang to sometime between 10⁻³³ and 10⁻³² seconds. Following the inflationary period, the Universe continues to expand, but at a less accelerated rate.^[1]

The inflationary hypothesis was developed in the 1980s by physicists Alan Guth and Andrei Linde.^[2] It explains the origin of the large-scale structure of the cosmos. Quantum fluctuations in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the Universe (see galaxy formation and evolution and structure formation).^[3] Many physicists also believe that inflation explains why the Universe appears to be the same in all directions (isotropic), why the cosmic microwave background radiation is distributed evenly, why the Universe is flat, and why no magnetic monopoles have been observed.

While the detailed particle physics mechanism responsible for inflation is not known, the basic picture makes a number of predictions that have been confirmed by observation.^[4][5] The hypothetical field thought to be responsible for inflation is called the inflaton.^[6]

Overview

An expanding universe generally has a cosmological horizon, which, by analogy with the more familiar horizon caused by the curvature of the Earth's surface, marks the boundary of the part of the Universe that an observer can see. Light (or other radiation) emitted by objects beyond the cosmological horizon never reaches the observer, because the space in between the observer and the object is expanding too rapidly.

History of the Universe - gravitational waves are hypothesized to arise from cosmic inflation, a faster-than-light expansion just after the Big Bang (17 March 2014).^[7][8][9]

The observable universe is one causal patch of a much larger unobservable universe; there are parts of the Universe that cannot communicate with us yet. These parts of the Universe are outside our current cosmological horizon. In the standard hot big bang model, without inflation, the cosmological horizon moves out, bringing new regions into view^{[citation needed]}. Yet as a local observer sees these regions for the first time, they look no different from any other region of space the local observer has already seen: they have a background radiation that is at nearly exactly the same temperature as the background radiation of other regions, and their space-time curvature is evolving lock-step with ours. This presents a mystery: how did these new regions know what temperature and curvature they were supposed to have? They couldn't have learned it by getting signals, because they were not in communication with our past light cone before.^[10][11]

Inflation answers this question by postulating that all the regions come from an earlier era with a big vacuum energy, or cosmological constant. A space with a cosmological constant is qualitatively different: instead of moving outward, the cosmological horizon stays put. For any one observer, the distance to the cosmological horizon is constant. With exponentially expanding space, two nearby observers are separated very quickly; so much so, that the distance between them quickly exceeds the limits of communications. The spatial slices are expanding very fast to cover huge volumes. Things are constantly moving beyond the cosmological horizon, which is a fixed distance away, and everything becomes homogeneous very quickly.

As the inflationary field slowly relaxes to the vacuum, the cosmological constant goes to zero, and space begins to expand normally. The new regions that come into view during the normal expansion phase are exactly the same regions that were pushed out of the horizon during inflation, and so they are necessarily at nearly the same temperature and curvature, because they come from the same little patch of space.

The theory of inflation thus explains why the temperatures and curvatures of different regions are so nearly equal. It also predicts that the total curvature of a space-slice at constant global time is zero. This prediction implies that the total ordinary matter, dark matter, and residual vacuum energy in the Universe have to add up to the critical density, and the evidence strongly supports this. More strikingly, inflation allows physicists to calculate the minute differences in temperature of different regions from quantum fluctuations during the inflationary era, and many of these quantitative predictions have been confirmed.^[12][13]

Space expands

To say that space expands exponentially means that two inertial observers are moving farther apart with accelerating velocity. In stationary coordinates for one observer, a patch of an inflating universe has the following polar metric:^[14][15]

This is just like an inside-out black hole metric—it has a zero in the component on a fixed radius sphere called the cosmological horizon. Objects are drawn away from the observer at towards the cosmological horizon, which they cross in a finite proper time. This means that any inhomogeneities are smoothed out, just as any bumps or matter on the surface of a black hole horizon are swallowed and disappear.

Since the space–time metric has no explicit time dependence, once an observer has crossed the cosmological horizon, observers closer in take its place. This process of falling outward and replacement points closer in are always steadily replacing points further out—an exponential expansion of space–time.

This steady-state exponentially expanding spacetime is called a de Sitter space, and to sustain it there must be a cosmological constant, a vacuum energy proportional to everywhere. In this case, the equation of state is . The physical conditions from one moment to the next are stable: the rate of expansion, called the Hubble parameter, is nearly constant, and the scale factor of the Universe is proportional to . Inflation is often called a period of accelerated expansion because the distance between two fixed observers is increasing exponentially (i.e. at an accelerating rate as they move apart), while can stay approximately constant (see deceleration parameter).

Few inhomogeneities remain

Cosmological inflation has the important effect of smoothing out inhomogeneities, anisotropies and the curvature of space. This pushes the Universe into a very simple state, in which it is completely dominated by the inflaton field, the source of the cosmological constant, and the only significant inhomogeneities are the tiny quantum fluctuations in the inflaton. Inflation also dilutes exotic heavy particles, such as the magnetic monopoles predicted by many extensions to the Standard Model of particle physics. If the Universe was only hot enough to form such particles before a period of inflation, they would not be observed in nature, as they would be so rare that it is quite likely that there are none in the observable universe. Together, these effects are called the inflationary "no-hair theorem"^[16] by analogy with the no hair theorem for black holes.

The "no-hair" theorem works essentially because the cosmological horizon is no different from a black-hole horizon, except for philosophical disagreements about what is on the other side. The interpretation of the no-hair theorem is that the Universe (observable and unobservable) expands by an enormous factor during inflation. In an expanding universe, energy densities generally fall, or get diluted, as the volume of the Universe increases. For example, the density of ordinary "cold" matter (dust) goes down as the inverse of the volume: when linear dimensions double, the energy density goes down by a factor of eight; the radiation energy density goes down even more rapidly as the Universe expands since the wavelength of each photon is stretched (redshifted), in addition to the photons being dispersed by the expansion. When linear dimensions are doubled, the energy density in radiation falls by a factor of sixteen (see the solution of the energy density continuity equation for an ultra-relativistic fluid).
During inflation, the energy density in the inflaton field is roughly constant. However, the energy density in everything else, including inhomogeneities, curvature, anisotropies, exotic particles, and standard-model particles is falling, and through sufficient inflation these all become negligible. This leaves the Universe flat and symmetric, and (apart from the homogeneous inflaton field) mostly empty, at the moment inflation ends and reheating begins.^[17]

Key requirement

A key requirement is that inflation must continue long enough to produce the present observable universe from a single, small inflationary Hubble volume. This is necessary to ensure that the Universe appears flat, homogeneous and isotropic at the largest observable scales. This requirement is generally thought to be satisfied if the Universe expanded by a factor of at least 10²⁶ during inflation.^[18]

Reheating

Inflation is a period of supercooled expansion, when the temperature drops by a factor of 100,000 or so. (The exact drop is model dependent, but in the first models it was typically from 10²⁷K down to 10²²K.^[19]) This relatively low temperature is maintained during the inflationary phase. When inflation ends the temperature returns to the pre-inflationary temperature; this is called reheating or thermalization because the large potential energy of the inflaton field decays into particles and fills the Universe with Standard Model particles, including electromagnetic radiation, starting the radiation dominated phase of the Universe. Because the nature of the inflation is not known, this process is still poorly understood, although it is believed to take place through a parametric resonance.^[20][21]

Motivations

Inflation resolves several problems in the Big Bang cosmology that were discovered in the 1970s.^[22] Inflation was first discovered by Guth while investigating the problem of why no magnetic monopoles are seen today; he found that a positive-energy false vacuum would, according to general relativity, generate an exponential expansion of space. It was very quickly realised that such an expansion would resolve many other long-standing problems. These problems arise from the observation that to look like it does today, the Universe would have to have started from very finely tuned, or "special" initial conditions at the Big Bang. Inflation attempts to resolve these problems by providing a dynamical mechanism that drives the Universe to this special state, thus making a universe like ours much more likely in the context of the Big Bang theory.

Horizon problem

The horizon problem is the problem of determining why the Universe appears statistically homogeneous and isotropic in accordance with the cosmological principle.^[23][24][25] For example, molecules in a canister of gas are distributed homogeneously and isotropically because they are in thermal equilibrium: gas throughout the canister has had enough time to interact to dissipate inhomogeneities and anisotropies. The situation is quite different in the big bang model without inflation, because gravitational expansion does not give the early universe enough time to equilibrate. In a big bang with only the matter and radiation known in the Standard Model, two widely separated regions of the observable universe cannot have equilibrated because they move apart from each other faster than the speed of light—thus have never come into causal contact: in the history of the Universe, back to the earliest times, it has not been possible to send a light signal between the two regions. Because they have no interaction, it is difficult to explain why they have the same temperature (are thermally equilibrated). This is because the Hubble radius in a radiation or matter-dominated universe expands much more quickly than physical lengths and so points that are out of communication are coming into communication. Historically, two proposed solutions were the Phoenix universe of Georges Lemaître^[26] and the related oscillatory universe of Richard Chase Tolman,^[27] and the Mixmaster universe of Charles Misner.^[24][28] Lemaître and Tolman proposed that a universe undergoing a number of cycles of contraction and expansion could come into thermal equilibrium. Their models failed, however, because of the buildup of entropy over several cycles. Misner made the (ultimately incorrect) conjecture that the Mixmaster mechanism, which made the Universe more chaotic, could lead to statistical homogeneity and isotropy.

Flatness problem

Another problem is the flatness problem (which is sometimes called one of the Dicke coincidences, with the other being the cosmological constant problem).^[29][30] It had been known in the 1960s that the density of matter in the Universe was comparable to the critical density necessary for a flat universe (that is, a universe whose large scale geometry is the usual Euclidean geometry, rather than a non-Euclidean hyperbolic or spherical geometry).^[31]:61
Therefore, regardless of the shape of the universe the contribution of spatial curvature to the expansion of the Universe could not be much greater than the contribution of matter. But as the Universe expands, the curvature redshifts away more slowly than matter and radiation. Extrapolated into the past, this presents a fine-tuning problem because the contribution of curvature to the Universe must be exponentially small (sixteen orders of magnitude less than the density of radiation at big bang nucleosynthesis, for example). This problem is exacerbated by recent observations of the cosmic microwave background that have demonstrated that the Universe is flat to the accuracy of a few percent.^[32]

Magnetic-monopole problem

The magnetic monopole problem (sometimes called the exotic-relics problem) says that if the early universe were very hot, a large number of very heavy^[why?], stable magnetic monopoles would be produced. This is a problem with Grand Unified Theories, which proposes that at high temperatures (such as in the early universe) the electromagnetic force, strong, and weak nuclear forces are not actually fundamental forces but arise due to spontaneous symmetry breaking from a single gauge theory.^[33] These theories predict a number of heavy, stable particles that have not yet been observed in nature. The most notorious is the magnetic monopole, a kind of stable, heavy "knot" in the magnetic field.^[34][35] Monopoles are expected to be copiously produced in Grand Unified Theories at high temperature,^[36][37] and they should have persisted to the present day, to such an extent that they would become the primary constituent of the Universe.^[38][39] Not only is that not the case, but all searches for them have failed, placing stringent limits on the density of relic magnetic monopoles in the Universe.^[40] A period of inflation that occurs below the temperature where magnetic monopoles can be produced would offer a possible resolution of this problem: monopoles would be separated from each other as the Universe around them expands, potentially lowering their observed density by many orders of magnitude. Though, as cosmologist Martin Rees has written, "Skeptics about exotic physics might not be hugely impressed by a theoretical argument to explain the absence of particles that are themselves only hypothetical. Preventive medicine can readily seem 100 percent effective against a disease that doesn't exist!"^[41]

History

Precursors

In the early days of General Relativity, Albert Einstein introduced the cosmological constant to allow a static solution, which was a three-dimensional sphere with a uniform density of matter. A little later, Willem de Sitter found a highly symmetric inflating universe, which described a universe with a cosmological constant that is otherwise empty.^[42] It was discovered that Einstein's solution is unstable, and if there are small fluctuations, it eventually either collapses or turns into de Sitter's.

In the early 1970s Zeldovich noticed the serious flatness and horizon problems of big bang cosmology; before his work, cosmology was presumed to be symmetrical on purely philosophical grounds.^{[citation needed]} In the Soviet Union, this and other considerations led Belinski and Khalatnikov to analyze the chaotic BKL singularity in General Relativity. Misner's Mixmaster universe attempted to use this chaotic behavior to solve the cosmological problems, with limited success.

In the late 1970s, Sidney Coleman applied the instanton techniques developed by Alexander Polyakov and collaborators to study the fate of the false vacuum in quantum field theory. Like a metastable phase in statistical mechanics—water below the freezing temperature or above the boiling point—a quantum field would need to nucleate a large enough bubble of the new vacuum, the new phase, in order to make a transition. Coleman found the most likely decay pathway for vacuum decay and calculated the inverse lifetime per unit volume. He eventually noted that gravitational effects would be significant, but he did not calculate these effects and did not apply the results to cosmology.

In the Soviet Union, Alexei Starobinsky noted that quantum corrections to general relativity should be important in the early universe. These generically lead to curvature-squared corrections to the Einstein–Hilbert action and a form of f(R) modified gravity. The solution to Einstein's equations in the presence of curvature squared terms, when the curvatures are large, leads to an effective cosmological constant. Therefore, he proposed that the early universe went through a de Sitter phase, an inflationary era.^[43] This resolved the problems of cosmology, and led to specific predictions for the corrections to the microwave background radiation, corrections that were calculated in detail shortly afterwards.

In 1978, Zeldovich noted the monopole problem, which was an unambiguous quantitative version of the horizon problem, this time in a fashionable subfield of particle physics, which led to several speculative attempts to resolve it. In 1980, working in the west, Alan Guth realized that false vacuum decay in the early universe would solve the problem, leading him to propose scalar driven inflation. Starobinsky's and Guth's scenarios both predicted an initial deSitter phase, differing only in the details of the mechanism.

Early inflationary models

According to Andrei Linde, the earliest theory of inflation was proposed by Erast Gliner (1965) but the theory was not taken seriously except by Andrei Sakharov, 'who made an attempt to calculate density perturbations produced in this scenario." ^[44] Independently, inflation was proposed in January 1980 by Alan Guth as a mechanism to explain the nonexistence of magnetic monopoles;^[45][46] it was Guth who coined the term "inflation".^[2] At the same time, Starobinsky argued that quantum corrections to gravity would replace the initial singularity of the Universe with an exponentially expanding deSitter phase.^[47] In October 1980, Demosthenes Kazanas suggested that exponential expansion could eliminate the particle horizon and perhaps solve the horizon problem,^[48] while Sato suggested that an exponential expansion could eliminate domain walls (another kind of exotic relic).^[49] In 1981 Einhorn and Sato^[50] published a model similar to Guth's and showed that it would resolve the puzzle of the magnetic monopole abundance in Grand Unified Theories. Like Guth, they concluded that such a model not only required fine tuning of the cosmological constant, but also would very likely lead to a much too granular universe, i.e., to large density variations resulting from bubble wall collisions.

The physical size of the Hubble radius (solid line) as a function of the linear expansion (scale factor) of the universe. During cosmological inflation, the Hubble radius is constant. The physical wavelength of a perturbation mode (dashed line) is also shown. The plot illustrates how the perturbation mode grows larger than the horizon during cosmological inflation before coming back inside the horizon, which grows rapidly during radiation domination. If cosmological inflation had never happened, and radiation domination continued back until a gravitational singularity, then the mode would never have been outside the horizon in the very early universe, and no causal mechanism could have ensured that the universe was homogeneous on the scale of the perturbation mode.

Guth proposed that as the early universe cooled, it was trapped in a false vacuum with a high energy density, which is much like a cosmological constant. As the very early universe cooled it was trapped in a metastable state (it was supercooled), which it could only decay out of through the process of bubble nucleation via quantum tunneling.
Bubbles of true vacuum spontaneously form in the sea of false vacuum and rapidly begin expanding at the speed of light. Guth recognized that this model was problematic because the model did not reheat properly: when the bubbles nucleated, they did not generate any radiation. Radiation could only be generated in collisions between bubble walls. But if inflation lasted long enough to solve the initial conditions problems, collisions between bubbles became exceedingly rare. In any one causal patch it is likely that only one bubble will nucleate.

Slow-roll inflation

The bubble collision problem was solved by Andrei Linde^[51] and independently by Andreas Albrecht and Paul Steinhardt^[52] in a model named new inflation or slow-roll inflation (Guth's model then became known as old inflation). In this model, instead of tunneling out of a false vacuum state, inflation occurred by a scalar field rolling down a potential energy hill. When the field rolls very slowly compared to the expansion of the Universe, inflation occurs. However, when the hill becomes steeper, inflation ends and reheating can occur.

Effects of asymmetries

Eventually, it was shown that new inflation does not produce a perfectly symmetric universe, but that tiny quantum fluctuations in the inflaton are created. These tiny fluctuations form the primordial seeds for all structure created in the later universe.^[53] These fluctuations were first calculated by Viatcheslav Mukhanov and G. V. Chibisov in the Soviet Union in analyzing Starobinsky's similar model.^[54][55][56] In the context of inflation, they were worked out independently of the work of Mukhanov and Chibisov at the three-week 1982 Nuffield Workshop on the Very Early Universe at Cambridge University.^[57] The fluctuations were calculated by four groups working separately over the course of the workshop: Stephen Hawking;^[58] Starobinsky;^[59] Guth and So-Young Pi;^[60] and James M. Bardeen, Paul Steinhardt and Michael Turner.^[61]

Observational status

Inflation is a mechanism for realizing the cosmological principle, which is the basis of the standard model of physical cosmology: it accounts for the homogeneity and isotropy of the observable universe. In addition, it accounts for the observed flatness and absence of magnetic monopoles. Since Guth's early work, each of these observations has received further confirmation, most impressively by the detailed observations of the cosmic microwave background made by the Wilkinson Microwave Anisotropy Probe (WMAP) spacecraft.^[12] This analysis shows that the Universe is flat to an accuracy of at least a few percent, and that it is homogeneous and isotropic to a part in 100,000.

In addition, inflation predicts that the structures visible in the Universe today formed through the gravitational collapse of perturbations that were formed as quantum mechanical fluctuations in the inflationary epoch. The detailed form of the spectrum of perturbations called a nearly-scale-invariant Gaussian random field (or Harrison–Zel'dovich spectrum) is very specific and has only two free parameters, the amplitude of the spectrum and the spectral index, which measures the slight deviation from scale invariance predicted by inflation (perfect scale invariance corresponds to the idealized de Sitter universe).^[62] Inflation predicts that the observed perturbations should be in thermal equilibrium with each other (these are called adiabatic or isentropic perturbations). This structure for the perturbations has been confirmed by the WMAP spacecraft and other cosmic microwave background experiments,^[12] and galaxy surveys, especially the ongoing Sloan Digital Sky Survey.^[63] These experiments have shown that the one part in 100,000 inhomogeneities observed have exactly the form predicted by theory. Moreover, there is evidence for a slight deviation from scale invariance. The spectral index, n_s is equal to one for a scale-invariant spectrum. The simplest models of inflation predict that this quantity is between 0.92 and 0.98.^{[64][65][66][67]} From the data taken by the WMAP spacecraft it can be inferred that n_s = 0.963 ± 0.012,^[68] implying that it differs from one at the level of two standard deviations (2σ). This is considered an important confirmation of the theory of inflation.^[12]

A number of theories of inflation have been proposed that make radically different predictions, but they generally have much more fine tuning than is necessary.^[64][65] As a physical model, however, inflation is most valuable in that it robustly predicts the initial conditions of the Universe based on only two adjustable parameters: the spectral index (that can only change in a small range) and the amplitude of the perturbations. Except in contrived models, this is true regardless of how inflation is realized in particle physics.

Occasionally, effects are observed that appear to contradict the simplest models of inflation. The first-year WMAP data suggested that the spectrum might not be nearly scale-invariant, but might instead have a slight curvature.^[69] However, the third-year data revealed that the effect was a statistical anomaly.^[12] Another effect has been remarked upon since the first cosmic microwave background satellite, the Cosmic Background Explorer: the amplitude of the quadrupole moment of the cosmic microwave background is unexpectedly low and the other low multipoles appear to be preferentially aligned with the ecliptic plane. Some have claimed that this is a signature of non-Gaussianity and thus contradicts the simplest models of inflation. Others have suggested that the effect may be due to other new physics, foreground contamination, or even publication bias.^[70]

An experimental program is underway to further test inflation with more precise measurements of the cosmic microwave background. In particular, high precision measurements of the so-called "B-modes" of the polarization of the background radiation could provide evidence of the gravitational radiation produced by inflation, and could also show whether the energy scale of inflation predicted by the simplest models (10¹⁵–10¹⁶ GeV) is correct.^[65][66]
In March 2014, it was announced that B-mode polarization of the background radiation consistent with that predicted from inflation had been demonstrated by a South Pole experiment, a collaboration led by four principal investigators from the California Institute of Technology, Harvard University, Stanford University, and the University of Minnesota BICEP2.^{[7][8][9][71][72][73]} However, on 19 June 2014, lowered confidence in confirming the findings was reported;^[72][74][75] on 19 September 2014, a further reduction in confidence was reported^[76][77] and, on 30 January 2015, even less confidence yet was reported.^[78][79]

Other potentially corroborating measurements are expected to be performed by the Planck spacecraft, although it is unclear if the signal will be visible, or if contamination from foreground sources will interfere with these measurements.^[80] Other forthcoming measurements, such as those of 21 centimeter radiation (radiation emitted and absorbed from neutral hydrogen before the first stars turned on), may measure the power spectrum with even greater resolution than the cosmic microwave background and galaxy surveys, although it is not known if these measurements will be possible or if interference with radio sources on Earth and in the galaxy will be too great.^[81]

Dark energy is broadly similar to inflation, and is thought to be causing the expansion of the present-day universe to accelerate. However, the energy scale of dark energy is much lower, 10⁻¹² GeV, roughly 27 orders of magnitude less than the scale of inflation.

Theoretical status

In the early proposal of Guth, it was thought that the inflaton was the Higgs field, the field that explains the mass of the elementary particles.^[46] It is now believed by some that the inflaton cannot be the Higgs field^[82] although the recent discovery of the Higgs boson has increased the number of works considering the Higgs field as inflaton.^[83] One problem of this identification is the current tension with experimental data at the electroweak scale,^[84] which is currently under study at the Large Hadron Collider (LHC). Other models of inflation relied on the properties of grand unified theories.^[52] Since the simplest models of grand unification have failed, it is now thought by many physicists that inflation will be included in a supersymmetric theory like string theory or a supersymmetric grand unified theory. At present, while inflation is understood principally by its detailed predictions of the initial conditions for the hot early universe, the particle physics is largely ad hoc modelling. As such, though predictions of inflation have been consistent with the results of observational tests, there are many open questions about the theory.

Fine-tuning problem

One of the most severe challenges for inflation arises from the need for fine tuning in inflationary theories. In new inflation, the slow-roll conditions must be satisfied for inflation to occur. The slow-roll conditions say that the inflaton potential must be flat (compared to the large vacuum energy) and that the inflaton particles must have a small mass^{[clarification needed]}.^[85] In order for the new inflation theory of Linde, Albrecht and Steinhardt to be successful, therefore, it seemed that the Universe must have a scalar field with an especially flat potential and special initial conditions. However, there are ways to explain these fine-tunings. For example, classically scale invariant field theories, where scale invariance is broken by quantum effects, provide an explanation of the flatness of inflationary potentials, as long as the theory can be studied through perturbation theory.^[86]

Andrei Linde

Andrei Linde proposed a theory known as chaotic inflation in which he suggested that the conditions for inflation are actually satisfied quite generically and inflation will occur in virtually any universe that begins in a chaotic, high energy state and has a scalar field with unbounded potential energy.^[87] However, in his model the inflaton field necessarily takes values larger than one Planck unit: for this reason, these are often called large field models and the competing new inflation models are called small field models. In this situation, the predictions of effective field theory are thought to be invalid, as renormalization should cause large corrections that could prevent inflation.^[88]
This problem has not yet been resolved and some cosmologists argue that the small field models, in which inflation can occur at a much lower energy scale, are better models of inflation.^[89] While inflation depends on quantum field theory (and the semiclassical approximation to quantum gravity) in an important way, it has not been completely reconciled with these theories.

Robert Brandenberger has commented on fine-tuning in another situation.^[90] The amplitude of the primordial inhomogeneities produced in inflation is directly tied to the energy scale of inflation. There are strong suggestions that this scale is around 10¹⁶ GeV or 10⁻³ times the Planck energy. The natural scale is naïvely the Planck scale so this small value could be seen as another form of fine-tuning (called a hierarchy problem): the energy density given by the scalar potential is down by 10⁻¹² compared to the Planck density. This is not usually considered to be a critical problem, however, because the scale of inflation corresponds naturally to the scale of gauge unification.

Eternal inflation

In many models of inflation, the inflationary phase of the Universe's expansion lasts forever in at least some regions of the Universe. This occurs because inflating regions expand very rapidly, reproducing themselves. Unless the rate of decay to the non-inflating phase is sufficiently fast, new inflating regions are produced more rapidly than non-inflating regions. In such models most of the volume of the Universe at any given time is inflating. All models of eternal inflation produce an infinite multiverse, typically a fractal.
Although new inflation is classically rolling down the potential, quantum fluctuations can sometimes bring it back up to previous levels. These regions in which the inflaton fluctuates upwards expand much faster than regions in which the inflaton has a lower potential energy, and tend to dominate in terms of physical volume. This steady state, which first developed by Vilenkin,^[91] is called "eternal inflation". It has been shown that any inflationary theory with an unbounded potential is eternal.^{[92][not in citation given]} It is a popular conclusion among physicists that this steady state cannot continue forever into the past.^[93][94][95] The inflationary spacetime, which is similar to de Sitter space, is incomplete without a contracting region. However, unlike de Sitter space, fluctuations in a contracting inflationary space will collapse to form a gravitational singularity, a point where densities become infinite.
Therefore, it is necessary to have a theory for the Universe's initial conditions. Linde, however, believes inflation may be past eternal.^[96]

In eternal inflation, regions with inflation have an exponentially growing volume, while regions that are not inflating don't. This suggests that the volume of the inflating part of the Universe in the global picture is always unimaginably larger than the part that has stopped inflating, even though inflation eventually ends as seen by any single pre-inflationary observer. Scientists disagree about how to assign a probability distribution to this hypothetical anthropic landscape. If the probability of different regions is counted by volume, one should expect that inflation will never end, or applying boundary conditions that a local observer exists to observe it, that inflation will end as late as possible. Some physicists believe this paradox can be resolved by weighting observers by their pre-inflationary volume.

Initial conditions

Some physicists have tried to avoid the initial conditions problem by proposing models for an eternally inflating universe with no origin.^{[97][98][99][100]} These models propose that while the Universe, on the largest scales, expands exponentially it was, is and always will be, spatially infinite and has existed, and will exist, forever.

Other proposals attempt to describe the ex nihilo creation of the Universe based on quantum cosmology and the following inflation. Vilenkin put forth one such scenario.^[91] Hartle and Hawking offered the no-boundary proposal for the initial creation of the Universe in which inflation comes about naturally.^[101]

Alan Guth has described the inflationary universe as the "ultimate free lunch":^[102][103] new universes, similar to our own, are continually produced in a vast inflating background. Gravitational interactions, in this case, circumvent (but do not violate) the first law of thermodynamics (energy conservation) and the second law of thermodynamics (entropy and the arrow of time problem). However, while there is consensus that this solves the initial conditions problem, some have disputed this, as it is much more likely that the Universe came about by a quantum fluctuation.
Donald Page was an outspoken critic of inflation because of this anomaly.^[104] He stressed that the thermodynamic arrow of time necessitates low entropy initial conditions, which would be highly unlikely. According to them, rather than solving this problem, the inflation theory further aggravates it – the reheating at the end of the inflation era increases entropy, making it necessary for the initial state of the Universe to be even more orderly than in other Big Bang theories with no inflation phase.

Hawking and Page later found ambiguous results when they attempted to compute the probability of inflation in the Hartle-Hawking initial state.^[105] Other authors have argued that, since inflation is eternal, the probability doesn't matter as long as it is not precisely zero: once it starts, inflation perpetuates itself and quickly dominates the Universe.^{[106][107]:223–225} However, Albrecht and Lorenzo Sorbo have argued that the probability of an inflationary cosmos, consistent with today's observations, emerging by a random fluctuation from some pre-existent state, compared with a non-inflationary cosmos overwhelmingly favours the inflationary scenario, simply because the "seed" amount of non-gravitational energy required for the inflationary cosmos is so much less than any required for a non-inflationary alternative, which outweighs any entropic considerations.^[108]

Another problem that has occasionally been mentioned is the trans-Planckian problem or trans-Planckian effects.^[109] Since the energy scale of inflation and the Planck scale are relatively close, some of the quantum fluctuations that have made up the structure in our universe were smaller than the Planck length before inflation. Therefore, there ought to be corrections from Planck-scale physics, in particular the unknown quantum theory of gravity. There has been some disagreement about the magnitude of this effect: about whether it is just on the threshold of detectability or completely undetectable.^[110]

Hybrid inflation

Another kind of inflation, called hybrid inflation, is an extension of new inflation. It introduces additional scalar fields, so that while one of the scalar fields is responsible for normal slow roll inflation, another triggers the end of inflation: when inflation has continued for sufficiently long, it becomes favorable to the second field to decay into a much lower energy state.^[111]

In hybrid inflation, one of the scalar fields is responsible for most of the energy density (thus determining the rate of expansion), while the other is responsible for the slow roll (thus determining the period of inflation and its termination). Thus fluctuations in the former inflaton would not affect inflation termination, while fluctuations in the latter would not affect the rate of expansion. Therefore hybrid inflation is not eternal.^[112][113] When the second (slow-rolling) inflaton reaches the bottom of its potential, it changes the location of the minimum of the first inflaton's potential, which leads to a fast roll of the inflaton down its potential, leading to termination of inflation.

Inflation and string cosmology

The discovery of flux compactifications have opened the way for reconciling inflation and string theory.^[114] A new theory, called brane inflation suggests that inflation arises from the motion of D-branes^[115] in the compactified geometry, usually towards a stack of anti-D-branes. This theory, governed by the Dirac-Born-Infeld action, is very different from ordinary inflation. The dynamics are not completely understood. It appears that special conditions are necessary since inflation occurs in tunneling between two vacua in the string landscape. The process of tunneling between two vacua is a form of old inflation, but new inflation must then occur by some other mechanism.

Inflation and loop quantum gravity

When investigating the effects the theory of loop quantum gravity would have on cosmology, a loop quantum cosmology model has evolved that provides a possible mechanism for cosmological inflation. Loop quantum gravity assumes a quantized spacetime. If the energy density is larger than can be held by the quantized spacetime, it is thought to bounce back.

Inflation and generalized uncertainty principle (GUP)

The effects of generalized uncertainty principle (GUP) on the inflationary dynamics and the thermodynamics of the early Universe are studied.^[116] Using the GUP approach, Tawfik et al. evaluated the tensorial and scalar density fluctuations in the inflation era and compared them with the standard case. They found a good agreement with the Wilkinson Microwave Anisotropy Probe data. Assuming that a quantum gas of scalar particles is confined within a thin layer near the apparent horizon of the Friedmann-Lemaitre-Robertson-Walker Universe that satisfies the boundary condition, Tawfik et al. calculated the number and entropy densities and the free energy arising from the quantum states using the GUP approach. Furthermore, a qualitative estimation for effects of the quantum gravity on all these thermodynamic quantities was introduced.

Alternatives to inflation

The flatness and horizon problems are naturally solved in the Einstein-Cartan-Sciama-Kibble theory of gravity, without needing an exotic form of matter and introducing free parameters.^[117][118] This theory extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamical variable. The minimal coupling between torsion and Dirac spinors generates a spin-spin interaction that is significant in fermionic matter at extremely high densities. Such an interaction averts the unphysical Big Bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the Universe was contracting. The rapid expansion immediately after the Big Bounce explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic. As the density of the Universe decreases, the effects of torsion weaken and the Universe smoothly enters the radiation-dominated era.

There are models that explain some of the observations explained by inflation. However none of these "alternatives" has the same breadth of explanation as inflation, and still require inflation for a more complete fit with observation; they should therefore be regarded as adjuncts to inflation, rather than as alternatives.

String theory requires that, in addition to the three observable spatial dimensions, there exist additional dimensions that are curled up or compactified (see also Kaluza–Klein theory). Extra dimensions appear as a frequent component of supergravity models and other approaches to quantum gravity. This raised the contingent question of why four space-time dimensions became large and the rest became unobservably small. An attempt to address this question, called string gas cosmology, was proposed by Robert Brandenberger and Cumrun Vafa.^[119] This model focuses on the dynamics of the early universe considered as a hot gas of strings. Brandenberger and Vafa show that a dimension of spacetime can only expand if the strings that wind around it can efficiently annihilate each other. Each string is a one-dimensional object, and the largest number of dimensions in which two strings will generically intersect (and, presumably, annihilate) is three. Therefore, one argues that the most likely number of non-compact (large) spatial dimensions is three. Current work on this model centers on whether it can succeed in stabilizing the size of the compactified dimensions and produce the correct spectrum of primordial density perturbations. For a recent review, see^[120] The authors admits that their model "does not solve the entropy and flatness problems of standard cosmology ..... and we can provide no explanation for why the current universe is so close to being spatially flat".^[121]

The ekpyrotic and cyclic models are also considered adjuncts to inflation. These models solve the horizon problem through an expanding epoch well before the Big Bang, and then generate the required spectrum of primordial density perturbations during a contracting phase leading to a Big Crunch. The Universe passes through the Big Crunch and emerges in a hot Big Bang phase. In this sense they are reminiscent of the oscillatory universe proposed by Richard Chace Tolman: however in Tolman's model the total age of the Universe is necessarily finite, while in these models this is not necessarily so. Whether the correct spectrum of density fluctuations can be produced, and whether the Universe can successfully navigate the Big Bang/Big Crunch transition, remains a topic of controversy and current research. Ekpyrotic models avoid the magnetic monopole problem as long as the temperature at the Big Crunch/Big Bang transition remains below the Grand Unified Scale, as this is the temperature required to produce magnetic monopoles in the first place. As things stand, there is no evidence of any 'slowing down' of the expansion, but this is not surprising as each cycle is expected to last on the order of a trillion years.

Another adjunct, the varying speed of light model has also been theorized by Jean-Pierre Petit in 1988, John Moffat in 1992 as well Andreas Albrecht and João Magueijo in 1999, instead of superluminal expansion the speed of light was 60 orders of magnitude faster than its current value solving the horizon and homogeneity problems in the early universe.

Criticisms

Since its introduction by Alan Guth in 1980, the inflationary paradigm has become widely accepted. Nevertheless, many physicists, mathematicians, and philosophers of science have voiced criticisms, claiming untestable predictions and a lack of serious empirical support.^[106] In 1999, John Earman and Jesús Mosterín published a thorough critical review of inflationary cosmology, concluding, "we do not think that there are, as yet, good grounds for admitting any of the models of inflation into the standard core of cosmology."^[122]

In order to work, and as pointed out by Roger Penrose from 1986 on, inflation requires extremely specific initial conditions of its own, so that the problem (or pseudo-problem) of initial conditions is not solved: "There is something fundamentally misconceived about trying to explain the uniformity of the early universe as resulting from a thermalization process. [...] For, if the thermalization is actually doing anything [...] then it represents a definite increasing of the entropy. Thus, the universe would have been even more special before the thermalization than after."^[123] The problem of specific or "fine-tuned" initial conditions would not have been solved; it would have gotten worse.

A recurrent criticism of inflation is that the invoked inflation field does not correspond to any known physical field, and that its potential energy curve seems to be an ad hoc contrivance to accommodate almost any data obtainable. Paul J. Steinhardt, one of the founding fathers of inflationary cosmology, has recently become one of its sharpest critics. He calls 'bad inflation' a period of accelerated expansion whose outcome conflicts with observations, and 'good inflation' one compatible with them: "Not only is bad inflation more likely than good inflation, but no inflation is more likely than either.... Roger Penrose considered all the possible configurations of the inflaton and gravitational fields. Some of these configurations lead to inflation ... Other configurations lead to a uniform, flat universe directly – without inflation. Obtaining a flat universe is unlikely overall. Penrose's shocking conclusion, though, was that obtaining a flat universe without inflation is much more likely than with inflation – by a factor of 10 to the googol (10 to the 100) power!"^[106][107]

Atmospheric Sciences & Global Change Division Research Highlights

April 2015

Original link:  http://www.pnnl.gov/science/highlights/highlight.asp?id=3966

Unlocking Cloud Gridlock

Handling climate-important cumulus clouds, regardless of model scale

Researchers at PNNL developed a new way for global climate and weather forecasting models to represent cumulus clouds, accounting for updrafts and downdrafts in a manner that is far more accurate, regardless of the scale of the model.

 

Results: Even as computing power increases, current climate model formulas struggle to handle storm clouds at today's higher resolutions and smaller model grid sizes. Cumulus storm cloud systems are still only partially resolved. Armed with a new formula developed by a research team led by Pacific Northwest National Laboratory, scientists can now represent cumulus in grid sizes as fine as 2 kilometers to as coarse as 256 kilometers. The team's approach breaks the storm cloud gridlock by more accurately depicting how cumulus clouds transport moisture through the atmosphere.

"This study helps us understand the scale-dependency of moisture and heat transported by cumulus clouds," said Dr. Jiwen Fan, an atmospheric scientist at PNNL, who led the team. "Our new formulation improves how the vertical transport of moisture by cumulus clouds is depicted in climate models at all scales."
 
Why It Matters: Representing these ubiquitous storm clouds in large-scale global climate models is crucial to obtaining accurate simulation of the climate, how it varies, and how it could change in the future. The old formulas can miss vital information necessary for accurate weather and climate prediction. Published in the Journal of Geophysical Research: Atmospheres, the new approach accounts for the variability of strong lifting currents in cumulus clouds.
 
Methods: Researchers at PNNL and collaborators from Scripps Institution of Oceanography and NASA Langley Research Center plugged real-world data into the Weather Research and Forecasting (WRF) model to simulate three storms: two over the U.S. Southern Great Plains in May of 2011 during the Midlatitude Continental Convective Clouds Experiment and one in the western Pacific near Australia in January 2006 during the Tropical Warm Pool International Cloud Experiment. The scientists started with a model grid size of 1 kilometer over an area 560 kilometers square. The researchers divided that 560 by 560 kilometer region into smaller squares with the lengths of 2, 4, 8, 16, 32, 64, 128, 256, and 512 kilometers to emulate the WRF and climate model grid sizes, and then examined the vertical transport of moisture as a benchmark at each of these scales.

The researchers discovered that the vertical transport by the cumulus clouds that cannot be resolved is strongly dependent on grid size. Evaluating the conventional formula that is used to represent the unresolved transport in the climate model, they found that it underestimates the transport at all scales. The new formula's accounting for the variability of ascending motions in convective updrafts much more closely approximates the benchmark results at all scales.
 
What's Next? Scientists will add the new formula to the National Center for Atmospheric Research's Community Atmosphere Model to improve climate and weather modeling.
 
Acknowledgments
 
Sponsors: The research was sponsored by the U.S. Department of Energy's Office of Science Office of Biological and Environmental Research Earth System Modeling program, along with the Office of Advanced Scientific Computing Research's Scientific Discovery through Advanced Computing program. Additional funding was provided by NASA's Modeling, Analysis and Prediction Program.
 
Facilities: PNNL's Institutional Computing program and National Energy Research Scientific Computing Center provided computing resources for the simulations.
 
Research Team: Yi-Chin Liu, Jiwen Fan, and Steven Ghan, PNNL; Guang Zhang, Scripps Institution of Oceanography, University of California at San Diego; and Kuan-Man Xu, NASA Langley Research Center
 
Research Area: Climate & Earth Systems Science
 
Reference: Liu Y-C, J Fan, G Zhang, K-M Xu, and SJ Ghan. 2015. "Improving Representation of Convective Transport for Scale-Aware Parameterization, Part II: Analysis of Cloud-Resolving Model Simulations." Journal of Geophysical Research Atmospheres, accepted. DOI:10.1002/2014JD022145

Mother’s science-based view: Organics and Whole Foods are ‘scam of the decade’

Kavin Senapathy | January 4, 2015 | Genetic Literacy Project

 

“USDA Certified Organic.”

These words may conjure notions of wholesomeness, healthiness, freshness and responsible consumer habits. I myself have traversed an arc from skepticism of the touted benefits of organics, to a complete boycott.
As a mother, now with two children, pressure has been building to switch to an organic diet. To alleviate well-placed family concern, my husband and I started purchasing organic apples, strawberries, and some of the other fruits and vegetables from the Environmental Working Group’s “Dirty Dozen” list. Never mind that in my estimation, organic apples in our area are at least 50 percent more expensive than conventional.

So-called “Dirty Dozen” isn’t so dirty


Long story short, I’m glad I know better now. I’m not a fan of getting bamboozled. I have no qualms about saying that the EWG “Dirty Dozen” list is unsubstantiated. There is no compelling reason to buy organic, yes, even the Dirty Dozen. The Farmer’s Daughter USA does an excellent job explaining why the scientific methodology behind the EWG list is flawed. In addition to flawed methodology, the pesticide residue on conventional produce is only a miniscule fraction of the amount one would need to consume to have any discernible effect. For example, a child would have to consume an impossible 1,500 servings of conventional strawberries in one day before any effect occurred.

I will unabashedly say that “organic” food is the scam of the decade. We already know that organic food is no more nutritious than its conventional counterparts. You may be thinking, “Well, I buy organic to avoid toxic pesticides.” Alas, the idea that organic farming doesn’t use pesticides is brilliantly pervasive, and has likely helped the massive growth of the 63 billion dollar organic industry. In fact, organic farmers often have to use more so-called “natural” pesticides to achieve the same effect of synthetic pesticides. Just like conventional produce, organic produce shows pesticide residue in laboratory tests. Make no mistake, the pesticides used in organic farming are no safer than those used in conventional agriculture.

For me, boycotting organic is justified


I didn’t previously go as far boycotting organic, but I can no longer handle the pesky cognitive dissonance. Even after I learned that there is no reason to buy organic, I’d purchase organic bananas if the conventional fruit was too green. I’d pick out a box of organic cookies if it was on sale. Then, a slow resentment started to build. The word “organic,” often juxtaposed with other faddish words like “natural,” began to irk me. At least I knew that I was paying a premium for an empty image; a perpetually unfulfilled promise of added health, and a sorry excuse to feel righteous.

Many consumers purchasing these products don’t know better, so for that reason among others, I decided to opt out of this lie. Not only is there no tangible reason to buy organic, but it contributes to the sad weakness of America’s critical-thinking skills. The organic industry perpetuates the “natural is better” fallacy. Supporting this industry with my family’s money is like personally hindering scientific progress.

I’ve never set foot in a Whole Foods, and never will

If you shop at Whole Foods and care whatsoever what I think, don’t fret. I’ve heard from lots of people that it’s a really nice store with fancy cheeses, amazing bakery items, and a wide selection of ready-to-eat vegetarian options.
That’s fine my friends, go nuts (do they have really good nuts, too?) In my opinion, Whole Foods helps promote the pretentious, judgmental false dichotomy that non-GMO and organic foods are somehow healthy and wholesome, while regular old food is junk.

This company that grossed more than 14 billion dollars in fiscal year 2014 — almost the same revenue as Monsanto, although Whole Foods is growing faster — devotes an entire section of its website to how “Values Matter.” This is an extensive section that self-righteously implies that Whole Foods upholds and sets the standards for food consumption morality, and that all other grocers are merely followers. Whole Foods shoppers get to bask in the trickle-down effect of these so-called “values.” I would never have believed that Whole Foods actually had a “Values Matter Anthem.” Alas, this pompous anthem truly does exist.

Spare us the value judgement, Whole Foods. This type of moralizing emanates not just from Whole Foods, but from the larger organic movement over all. The Big Organic Behemoth’s rhetoric creates a deceptively discordant image of people who care about their health versus those buying conventional food. The tacit message is that those neglecting to buy organic are lazy, parsimonious, poor, or gluttonous. Perhaps the mom choosing conventional produce is selfish, and doesn’t care about her child’s well-being. This exploitation of guilt to sway parents to shell out for organic food is, sadly, quite pervasive.

GMO Free USA, please spare parents the unnecessary guilt trip.

These so-called “values” are completely ideological. Worse, Whole Foods is a leader in promoting the fallacy that GMOs should be avoided. The Whole Foods website states:

“We are the first national grocery chain to set a deadline for full GMO transparency and our GMO labeling go further than the state laws and initiatives for labeling that are pending. This means we are the first to do a lot of this work and will be paving the way for those who follow.”

This is clearly an attempt by Whole Foods to paint itself with the brush of a pioneer. It’s as if this company expects other grocery chains to thank Whole Foods for its seemingly groundbreaking work in GMO transparency. The truth is, this is yet another marketing ploy. The only way Whole Foods is paving is the way to scientific illiteracy.

As I’ve discussed previously, the overwhelming scientific consensus agrees that GMOs are safe. Genetic modification has the potential to feed and nourish the world’s growing population in the most sustainable manner possible.  I personally will no longer buy into the organic scam. The idea that parents like me don’t care about our kids is ludicrous. In fact, I WANT BETTER for my children. I want them to grow up knowing how to spend their money wisely. I want them to be able to smell a scam from a mile away. I want them to grow up in a more scientifically savvy country than America is today, and I’m doing my best to make that happen. My children love fruits and vegetables, but there is no way on this green, genetically dynamic earth that I’ll buy an organic fruit again. Except on the rarest of occasions like the other day when I bought organic apple juice by mistake. I’ll have to be more careful.

This piece was adapted from:  Why This Mom Boycotts Organic and Will Never Shop at Whole Foods
Kavin Senapathy is a contributor at Genetic Literacy Project. She works for a genomics and bioinformatics R&D in Madison, WI. Her interests span the human and agricultural realms. Opinions expressed are her own and do not reflect her employer. Follow Kavin on her science advocacy Facebook page, and Twitter @ksenapathy

Shape of the universe

From Wikipedia, the free encyclopedia

The shape of the Universe is the local and global geometry of the universe, in terms of both curvature and topology (though, strictly speaking, the concept goes beyond both). When physicists describe the Universe as being flat or nearly flat, they're talking geometry: how space and time are warped according to general relativity. When they talk about whether it is open or closed, they're referring to its topology.^[1] Although the shape of the Universe is still a matter of debate in physical cosmology, the recent Wilkinson Microwave Anisotropy Probe (WMAP) measurements allow the statement that "We now know that the universe is flat with only a 0.4% margin of error", according to NASA scientists. ^{[2] [3]} Theorists have been trying to construct a formal mathematical model of the shape of the Universe. In formal terms, this is a 3-manifold model corresponding to the spatial section (in comoving coordinates) of the 4-dimensional space-time of the Universe. The model most theorists currently use is the so-called Friedmann–Lemaître–Robertson–Walker (FLRW) model. According to cosmologists, on this model the observational data best fit with the conclusion that the shape of the Universe is infinite and flat,^[4] but the data are also consistent with other possible shapes, such as the so-called Poincaré dodecahedral space^[5][6] and the Picard horn.^[7]

Two aspects of shape

The local geometry of the Universe is determined by whether the density parameter Ω is greater than, less than, or equal to 1.
From top to bottom: a spherical universe with Ω > 1, a hyperbolic universe with Ω < 1, and a flat universe with Ω = 1. Note that these depictions of two-dimensional surfaces are merely easily visualizable analogs to the 3-dimensional structure of (local) space.

Describing the shape of the Universe requires a consideration of two aspects:

1. its local geometry, which mostly concerns the curvature of the Universe, particularly the observable universe, and
2. its global geometry, which concerns the topology of the Universe as a whole.

If the observable universe encompasses the entire universe, we may be able to determine the global structure of the entire universe by observation. However, if the observable universe is smaller than the entire universe, our observations will be limited to only a part of the whole, and we may not be able to determine its global geometry through measurement. It is possible to construct different mathematical models of the global geometry of the entire universe all of which are consistent with current observational data. For example, the observable universe may be many orders of magnitude smaller than the entire universe. The Universe may be small in some dimensions and not in others (analogous to the way a cuboid is longer in the dimension of length than it is in the dimensions of width and depth). To test whether a given mathematical model describes the Universe accurately, scientists look for the model's novel implications—what are some phenomena in the Universe that we have not yet observed, but that must exist if the model is correct—and they devise experiments to test whether those phenomena occur or not. For example, if the Universe is a small closed loop, one would expect to see multiple images of an object in the sky, although not necessarily images of the same age.

Cosmologists normally work with a given space-like slice of spacetime called the comoving coordinates, the existence of a preferred set of which is possible and widely accepted in present-day physical cosmology. The section of spacetime that can be observed is the backward light cone (all points within the cosmic light horizon, given time to reach a given observer), while the related term Hubble volume can be used to describe either the past light cone or comoving space up to the surface of last scattering. To speak of "the shape of the universe (at a point in time)" is ontologically naive from the point of view of special relativity alone: due to the relativity of simultaneity we cannot speak of different points in space as being "at the same point in time" nor, therefore, of "the shape of the universe at a point in time".

Local geometry (spatial curvature)

The local geometry is the curvature describing any arbitrary point in the observable universe (averaged on a sufficiently large scale). Many astronomical observations, such as those from supernovae and the Cosmic Microwave Background (CMB) radiation, show the observable universe to be very close to homogeneous and isotropic and infer it to be accelerating.

FLRW model of the universe

In General Relativity, this is modelled by the Friedmann–Lemaître–Robertson–Walker (FLRW) model. This model, which can be represented by the Friedmann equations, provides a curvature (often referred to as geometry) of the Universe based on the mathematics of fluid dynamics, i.e. it models the matter within the Universe as a perfect fluid. Although stars and structures of mass can be introduced into an "almost FLRW" model, a strictly FLRW model is used to approximate the local geometry of the observable universe.

Another way of saying this is that if all forms of dark energy are ignored, then the curvature of the Universe can be determined by measuring the average density of matter within it, assuming that all matter is evenly distributed (rather than the distortions caused by 'dense' objects such as galaxies).

This assumption is justified by the observations that, while the Universe is "weakly" inhomogeneous and anisotropic (see the large-scale structure of the cosmos), it is on average homogeneous and isotropic.

The homogeneous and isotropic universe allows for a spatial geometry with a constant curvature. One aspect of local geometry to emerge from General Relativity and the FLRW model is that the density parameter, Omega (Ω), is related to the curvature of space. Omega is the average density of the Universe divided by the critical energy density, i.e. that required for the Universe to be flat (zero curvature).

The curvature of space is a mathematical description of whether or not the Pythagorean theorem is valid for spatial coordinates. In the latter case, it provides an alternative formula for expressing local relationships between distances:

• If the curvature is zero, then Ω = 1, and the Pythagorean theorem is correct;
• If Ω < 1, there is positive curvature; and
• if Ω < 1 there is negative curvature.

In the last two cases, the Pythagorean theorem is invalid (but discrepancies are only detectable in triangles whose sides' lengths are of cosmological scale).

If you measure the circumferences of circles of steadily larger diameters and divide the former by the latter, all three geometries give a value very close to π for small enough diameters but the ratio departs from π for larger diameters unless Ω = 1:

• For Ω < 1 (the sphere, see diagram) the ratio falls below π: indeed, a great circle on a sphere has circumference only twice its diameter.
• For Ω < 1 the ratio rises above π.

Astronomical measurements of both matter-energy density of the Universe and spacetime intervals using supernova events constrain the spatial curvature to be very close to zero, although they do not constrain its sign. This means that although the local geometries of spacetime are generated by the theory of relativity based on spacetime intervals, we can approximate 3-space by the familiar Euclidean geometry.

Possible local geometries

There are three categories for the possible spatial geometries of constant curvature, depending on the sign of the curvature. If the curvature is exactly zero, then the local geometry is flat; if it is positive, then the local geometry is spherical, and if it is negative then the local geometry is hyperbolic.

The geometry of the Universe is usually represented in the system of comoving coordinates, according to which the expansion of the Universe can be ignored. Comoving coordinates form a single frame of reference according to which the Universe has a static geometry of three spatial dimensions.

Under the assumption that the Universe is homogeneous and isotropic, the curvature of the observable universe, or the local geometry, is described by one of the three "primitive" geometries (in mathematics these are called the model geometries):

• 3-dimensional Flat Euclidean geometry, generally notated as E³
• 3-dimensional spherical geometry with a small curvature, often notated as S³
• 3-dimensional hyperbolic geometry with a small curvature

Even if the Universe is not exactly spatially flat, the spatial curvature is close enough to zero to place the radius at approximately the horizon of the observable universe or beyond.

Global structure: geometry and topology

Global structure covers the geometry and the topology of the whole universe—both the observable universe and beyond. While the local geometry does not determine the global geometry completely, it does limit the possibilities, particularly a geometry of a constant curvature. For this discussion, the Universe is taken to be a geodesic manifold, free of topological defects; relaxing either of these complicates the analysis considerably.

A global geometry is a local geometry plus a topology. It follows that a topology alone does not give a global geometry: for instance, Euclidean 3-space and hyperbolic 3-space have the same topology but different global geometries.

Investigations within the study of global structure of include

• Whether the Universe is infinite or finite in extent
• The scale or size of the entire universe (if it is finite)
• Whether the geometry is flat, positively curved, or negatively curved
• Whether the topology is simply connected like a sphere or multiply connected like a torus

Infinite or finite

One of the presently unanswered questions about the Universe is whether it is infinite or finite in extent.
Mathematically, the question of whether the Universe is infinite or finite is referred to as boundedness. An infinite universe (unbounded metric space) means that there are points arbitrarily far apart: for any distance d, there are points that are of a distance at least d apart. A finite universe is a bounded metric space, where there is some distance d such that all points are within distance d of each other. The smallest such d is called the diameter of the Universe, in which case the Universe has a well-defined "volume" or "scale."

Closed manifolds

Many finite mathematical spaces, e.g. a disc, have an edge or boundary. Spaces that have an edge are difficult to treat, both conceptually and mathematically. Namely, it is very difficult to state what would happen at the edge of such a universe. For this reason, spaces that have an edge are typically excluded from consideration. However, there exist many finite spaces, such as the 3-sphere and 3-torus, which have no edges. Mathematically, these spaces are referred to as being compact without boundary. The term compact basically means that it is finite in extent ("bounded") and is a closed set. The term "without boundary" means that the space has no edges. Moreover, so that calculus can be applied, the Universe is typically assumed to be a differentiable manifold. A mathematical object that possess all these properties, compact without boundary and differentiable, is termed a closed manifold. The 3-sphere and 3-torus are both closed manifolds.

Scale

For spherical and hyperbolic spatial geometries, the curvature gives a scale (either by using the radius of curvature or its inverse), a fact noted by Carl Friedrich Gauss in an 1824 letter to Franz Taurinus.^[8]

For a flat spatial geometry, the scale of any properties of the topology is arbitrary and may or may not be directly detectable.

The probability of detection of the topology by direct observation depends on the spatial curvature: a small curvature of the local geometry, with a corresponding radius of curvature greater than the observable horizon, makes the topology difficult or impossible to detect if the curvature is hyperbolic. A spherical geometry with a small curvature (large radius of curvature) does not make detection difficult.

Analysis of data from WMAP implies that on the scale to the surface of last scattering, the density parameter of the Universe is within about 0.5% of the value representing spatial flatness.^[9]

Curvature

The curvature of the Universe places constraints on the topology. If the spatial geometry is spherical, i.e. possess positive curvature, the topology is compact. For a flat (zero curvature) or a hyperbolic (negative curvature) spatial geometry, the topology can be either compact or infinite.^[10] Many textbooks erroneously state that a flat universe implies an infinite universe; however, the correct statement is that a flat universe that is also simply connected implies an infinite universe.^[10] For example, Euclidean space is flat, simply connected and infinite, but the torus is flat, multiply connected, finite and compact.

In general, local to global theorems in Riemannian geometry relate the local geometry to the global geometry. If the local geometry has constant curvature, the global geometry is very constrained, as described in Thurston geometries.

The latest research shows that even the most powerful future experiments (like SKA, Planck..) will not be able to distinguish between flat, open and closed universe if the true value of cosmological curvature parameter is smaller than 10⁻⁴. If the true value of the cosmological curvature parameter is larger than 10⁻³ we will be able to distinguish between these three models even now.^[11]

Results of the Planck mission released in 2015 show the cosmological curvature parameter, Ω_K, to be 0.000±0.005, coincident with a flat Universe.^[12]

Universe with zero curvature

In a universe with zero curvature, the local geometry is flat. The most obvious global structure is that of Euclidean space, which is infinite in extent. Flat universes that are finite in extent include the torus and Klein bottle. Moreover, in three dimensions, there are 10 finite closed flat 3-manifolds, of which 6 are orientable and 4 are non-orientable. The most familiar is the aforementioned 3-Torus universe.

In the absence of dark energy, a flat universe expands forever but at a continually decelerating rate, with expansion asymptotically approaching zero. With dark energy, the expansion rate of the Universe initially slows down, due to the effect of gravity, but eventually increases. The ultimate fate of the universe is the same as that of an open universe.

A flat universe can have zero total energy.

Universe with positive curvature

A positively curved universe is described by spherical geometry, and can be thought of as a three-dimensional hypersphere, or some other spherical 3-manifold (such as the Poincaré dodecahedral space), all of which are quotients of the 3-sphere.

Poincaré dodecahedral space, a positively curved space, colloquially described as "soccerball-shaped", as it is the quotient of the 3-sphere by the binary icosahedral group, which is very close to icosahedral symmetry, the symmetry of a soccer ball. This was proposed by Jean-Pierre Luminet and colleagues in 2003^[5][13] and an optimal orientation on the sky for the model was estimated in 2008.^[6]

Universe with negative curvature

A hyperbolic universe, one of a negative spatial curvature, is described by hyperbolic geometry, and can be thought of locally as a three-dimensional analog of an infinitely extended saddle shape. There are a great variety of hyperbolic 3-manifolds, and their classification is not completely understood. For hyperbolic local geometry, many of the possible three-dimensional spaces are informally called horn topologies, so called because of the shape of the pseudosphere, a canonical model of hyperbolic geometry. An example is the Picard horn, a negatively curved space, colloquially described as "funnel-shaped".^[7]

Curvature: Open or closed

When cosmologists speak of the Universe as being "open" or "closed", they most commonly are referring to whether the curvature is negative or positive. These meanings of open and closed are different from the mathematical meaning of open and closed used for sets in metric spaces and for the mathematical meaning of open and closed manifolds, which gives rise to ambiguity and confusion. In mathematics, there are definitions for a closed manifold (i.e. compact without boundary) and open manifold (i.e. one that is not compact and without boundary,^[14]). A "closed universe" is necessarily a closed manifold. An "open universe" can be either a closed or open manifold. For example, the Friedmann–Lemaître–Robertson–Walker (FLRW) model the Universe is considered to be without boundaries, in which case "compact universe" could describe a universe that is a closed manifold.

Milne model ("spherical" expanding)

Universe in an expanding sphere. The galaxies farthest away are moving fastest and hence experience length contraction and so become smaller to an observer in the centre.

If one applies Minkowski space-based Special Relativity to expansion of the Universe, without resorting to the concept of a curved spacetime, then one obtains the Milne model. Any spatial section of the Universe of a constant age (the proper time elapsed from the Big Bang) will have a negative curvature; this is merely a pseudo-Euclidean geometric fact analogous to one that concentric spheres in the flat Euclidean space are nevertheless curved. Spacial geometry of this model is an unbounded hyperbolic space. The entire universe is contained within a light cone, namely the future cone of the Big Bang. For any given moment t > 0 of coordinate time (assuming the Big Bang has t = 0), the entire universe is bounded by a sphere of radius exactly c t. The apparent paradox of an infinite universe contained within a sphere is explained with length contraction: the galaxies farther away, which are travelling away from the observer the fastest, will appear thinner.

This model is essentially a degenerate FLRW for Ω = 0. It is incompatible with observations that definitely rule out such a large negative spatial curvature. However, as a background in which gravitational fields (or gravitons) can operate, due to diffeomorphism invariance, the space on the macroscopic scale, is equivalent to any other (open) solution of Einstein's field equations.

rigins of Complex Life Uncovered in the Ocean Deep

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Posted by R.A. Becker on Thu, 07 May 2015

Original link:  http://www.pbs.org/wgbh/nova/next/evolution/origins-of-complex-life-uncovered-in-the-ocean-deep/

Scientists have just discovered a missing link between two branches on the evolutionary tree of life hiding deep under the sea, one that we’ve been looking for since 1977.

Ever since microbiologist Carl Woese, the greatest scientist you’ve never heard of, added a third branch, archaea, to the existing two of prokaryotes (bacteria) and eukaryotes (which have more complex cells like our own), scientists have searched for the evolutionary connection between archaea and eukaryotes. While the reigning theory is that eukaryotes evolved from the simpler archaea, the ancestral parent of eukaryotes has remained elusive.

Scientists discovered the closest evolutionary relative to eukaryotic cells near a hydrothermal vent.

But just this week, a group of scientists announced that they found that connection buried under the Arctic Ocean near a hydrothermal vent called Loki’s Castle. They named it Lokiarchaeum, and published their findings in the journal Nature.

Here’s Carl Zimmer, reporting for the New York Times:

Analyzing the DNA, the researchers found that Lokiarchaeum is far more closely related to eukaryotes than any other known species of archaea. But even more surprising was that it had genes for many traits only found before in eukaryotes.Among these genes were many that build special compartments inside eukaryote cells. Inside these compartments, called lysosomes, eukaryote cells can destroy defective proteins.

All eukaryotes also share a cellular skeleton that they constantly build and tear down to change their shape. Dr. Ettema and his colleagues found many genes in Lokiarchaeum that encode the proteins required to build the skeleton.

The scientists are now trying to grow these cells in the lab to understand more about them, but it’s difficult to replicate the conditions of deep ocean hydrothermal vents. In the meantime they’re looking for more archaea that might be even closer relatives of our eukaryotic ancestors, and in turn telling us more about our own origins.

Eternal inflation

From Wikipedia, the free encyclopedia

The eternal nature of new inflation was discovered independently by Paul Steinhardt and Alexander Vilenkin in 1983.^[1] Eternal inflation is an inflationary universe model, which is itself an outgrowth or extension of the Big Bang theory. In theories of eternal inflation, the inflationary phase of the universe's expansion lasts forever in at least some regions of the universe. Because these regions expand exponentially rapidly, most of the volume of the universe at any given time is inflating. All models of eternal inflation produce an infinite multiverse, typically a fractal.

Eternal inflation is predicted by many different models of cosmic inflation. MIT professor Alan H. Guth proposed an inflation model involving a "false vacuum" phase with positive vacuum energy. Parts of the universe in that phase inflate, and only occasionally decay to lower-energy, non-inflating phases or the ground state. In chaotic inflation, proposed by physicist Andrei Linde, the peaks in the evolution of a scalar field (determining the energy of the vacuum) correspond to regions of rapid inflation which dominate. Chaotic inflation usually eternally inflates,^[2] since the expansions of the inflationary peaks exhibit positive feedback and come to dominate the large-scale dynamics of the universe.

Alan Guth's 2007 paper, "Eternal inflation and its implications",^[2] details what is now known on the subject, and demonstrates that this particular flavor of inflationary universe theory is relatively current, or is still considered viable, more than 20 years after its inception.^{[3] [4][5]}

Inflation and the multiverse

Both Linde and Guth believe that inflationary models of the early universe most likely lead to a multiverse but more proof is required.

It's hard to build models of inflation that don't lead to a multiverse. It's not impossible, so I think there's still certainly research that needs to be done. But most models of inflation do lead to a multiverse, and evidence for inflation will be pushing us in the direction of taking [the idea of a] multiverse seriously. Alan Guth^[6]

It's possible to invent models of inflation that do not allow [a] multiverse, but it's difficult. Every experiment that brings better credence to inflationary theory brings us much closer to hints that the multiverse is real. Andrei Linde ^[6]

Polarization in the cosmic microwave background radiation suggests inflationary models for the early universe are more likely but confirmation is needed.^[6]

History

Inflation, or the inflationary universe theory, was developed as a way to overcome the few remaining problems with what was otherwise considered a successful theory of cosmology, the Big Bang model. Although Alexei Starobinsky of the L.D. Landau Institute of Theoretical Physics in Moscow developed the first realistic inflation theory in 1979^[7][8] he did not articulate its relevance to modern cosmological problems.

In 1979, Alan Guth developed an inflationary model independently, which offered a mechanism for inflation to begin: the decay of a so-called false vacuum into "bubbles" of "true vacuum" that expanded at the speed of light. Guth coined the term "inflation", and he was the first to discuss the theory with other scientists worldwide. But this formulation was problematic, as there was no consistent way to bring an end to the inflationary epoch and end up with the isotropic, homogeneous universe observed today. (See False vacuum: Development of theories). In 1982, this "graceful exit problem" was solved by Andrei Linde in the new inflationary scenario. A few months later, the same result was also obtained by Andreas Albrecht and Paul J. Steinhardt.

In 1986, Linde published an alternative model of inflation that also reproduced the same successes of new inflation entitled "Eternally Existing Self-Reproducing Chaotic Inflationary Universe",^[9] which provides a detailed description of what has become known as the Chaotic Inflation theory or eternal inflation. The Chaotic Inflation theory is in some ways similar to Fred Hoyle’s steady state theory, as it employs the concept of a universe that is eternally existing, and thus does not require a unique beginning or an ultimate end of the cosmos.

Quantum fluctuations of the inflation field

Chaotic Inflation theory models quantum fluctuations in the rate of inflation.^[10] Those regions with a higher rate of inflation expand faster and dominate the universe, despite the natural tendency of inflation to end in other regions. This allows inflation to continue forever, to produce future-eternal inflation.

Within the framework of established knowledge of physics and cosmology, our universe could be one of many in a super-universe or multiverse. Linde (1990, 1994) has proposed that a background space-time "foam" empty of matter and radiation will experience local quantum fluctuations in curvature, forming many bubbles of false vacuum that individually inflate into mini-universes with random characteristics. Each universe within the multiverse can have a different set of constants and physical laws. Some might have life of a form different from ours; others might have no life at all or something even more complex or so different that we cannot even imagine it. Obviously we are in one of those universes with life.^[11]

—Victor J. Stenger

Past-eternal models have been proposed which adhere to the perfect cosmological principle and have features of the steady state cosmos.^[12][13][14]

A recent paper by Kohli and Haslam^{[when?] [15]} analyzed Linde's chaotic inflation theory in which the quantum fluctuations are modelled as Gaussian white noise. They showed that in this popular scenario, eternal inflation in fact cannot be eternal, and the random noise leads to spacetime being filled with singularities. This was demonstrated by showing that solutions to the Einstein field equations diverge in a finite time. Their paper therefore concluded that the theory of eternal inflation based on random quantum fluctuations would not be a viable theory, and the resulting existence of a multiverse is "still very much an open question that will require much deeper investigation".

Differential decay

In standard inflation, inflationary expansion occurred while the universe was in a false vacuum state, halting when the universe decayed to a true vacuum state and became a general and inclusive phenomenon with homogeneity throughout, yielding a single expanding universe which is "our general reality" wherein the laws of physics are consistent throughout. In this case, the physical laws "just happen" to be compatible with the evolution of life.

The bubble universe model proposes that different regions of this inflationary universe (termed a multiverse) decayed to a true vacuum state at different times, with decaying regions corresponding to "sub"- universes not in causal contact with each other and existing in discrete regions that are subject to truly random "selection", determining each region's components based upon the persistence of the quantum components within that region. The end result will be a finite number of universes with physical laws consistent within each region of spacetime.

False vacuum and true vacuum

Variants of the bubble universe model postulate multiple false vacuum states, which result in lower-energy false-vacuum "progeny" universes spawned, which in turn produce true vacuum state progeny universes within themselves.

Evidence from the fluctuation level in our universe

New inflation does not produce a perfectly symmetric universe; tiny quantum fluctuations in the inflaton are created. These tiny fluctuations form the primordial seeds for all structure created in the later universe. These fluctuations were first calculated by Viatcheslav Mukhanov and G. V. Chibisov in the Soviet Union in analyzing Starobinsky's similar model.^[16][17][18] In the context of inflation, they were worked out independently of the work of Mukhanov and Chibisov at the three-week 1982 Nuffield Workshop on the Very Early Universe at Cambridge University.^[19] The fluctuations were calculated by four groups working separately over the course of the workshop: Stephen Hawking;^[20] Starobinsky;^[21] Guth and So-Young Pi;^[22] and James M. Bardeen, Paul Steinhardt and Michael Turner.^[23]

The fact that these models are consistent with WMAP data adds weight to the idea that the universe could be created in such a way. As a result, many physicists in the field agree it is possible, but needs further support to be accepted.^[24]

Graviton

From Wikipedia, the free encyclopedia

Graviton

Composition	Elementary particle
Statistics	Bose–Einstein statistics
Interactions	Gravitation
Status	Theoretical
Symbol	G[1]
Antiparticle	Self
Theorized	1930s[2] The name is attributed to Dmitrii Blokhintsev and F. M. Gal'perin in 1934[3]
Discovered	Hypothetical
Mass	0
Mean lifetime	Stable
Electric charge	0 e
Spin	2

In physics, the graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton is expected to be massless (because the gravitational force appears to have unlimited range) and must be a spin-2 boson. The spin follows from the fact that the source of gravitation is the stress–energy tensor, a second-rank tensor (compared to electromagnetism's spin-1 photon, the source of which is the four-current, a first-rank tensor). Additionally, it can be shown that any massless spin-2 field would give rise to a force indistinguishable from gravitation, because a massless spin-2 field must couple to (interact with) the stress–energy tensor in the same way that the gravitational field does. Seeing as the graviton is hypothetical, its discovery would unite quantum theory with gravity.^[4] This result suggests that, if a massless spin-2 particle is discovered, it must be the graviton, so that the only experimental verification needed for the graviton may simply be the discovery of a massless spin-2 particle.^[5]

Theory

The four other known forces of nature are mediated by elementary particles: electromagnetism by the photon, the strong interaction by the gluons, the Higgs field by the Higgs Boson, and the weak interaction by the W and Z bosons. The hypothesis is that the gravitational interaction is likewise mediated by an – as yet undiscovered – elementary particle, dubbed as the graviton. In the classical limit, the theory would reduce to general relativity and conform to Newton's law of gravitation in the weak-field limit.^[6][7][8]

Gravitons and renormalization

When describing graviton interactions, the classical theory (i.e., the tree diagrams) and semiclassical corrections (one-loop diagrams) behave normally, but Feynman diagrams with two (or more) loops lead to ultraviolet divergences; that is, infinite results that cannot be removed because the quantized general relativity is not renormalizable, unlike quantum electrodynamics.^{[dubious – discuss]} That is, the usual ways physicists calculate the probability that a particle will emit or absorb a graviton give nonsensical answers and the theory loses its predictive power. These problems, together with some conceptual puzzles, led many physicists^[who?] to believe that a theory more complete than quantized general relativity must describe the behavior near the Planck scale.^{[citation needed]}

Comparison with other forces

Unlike the force carriers of the other forces, gravitation plays a special role in general relativity in defining the spacetime in which events take place. In some descriptions, matter modifies the 'shape' of spacetime itself, and gravity is a result of this shape, an idea which at first glance may appear hard to match with the idea of a force acting between particles.^[9] Because the diffeomorphism invariance of the theory does not allow any particular space-time background to be singled out as the "true" space-time background, general relativity is said to be background independent. In contrast, the Standard Model is not background independent, with Minkowski space enjoying a special status as the fixed background space-time.^[10] A theory of quantum gravity is needed in order to reconcile these differences.^[11] Whether this theory should be background independent is an open question. The answer to this question will determine our understanding of what specific role gravitation plays in the fate of the universe.^[12]

Gravitons in speculative theories

String theory predicts the existence of gravitons and their well-defined interactions. A graviton in perturbative string theory is a closed string in a very particular low-energy vibrational state. The scattering of gravitons in string theory can also be computed from the correlation functions in conformal field theory, as dictated by the AdS/CFT correspondence, or from matrix theory.^{[citation needed]}

An interesting feature of gravitons in string theory is that, as closed strings without endpoints, they would not be bound to branes and could move freely between them. If we live on a brane (as hypothesized by brane theories) this "leakage" of gravitons from the brane into higher-dimensional space could explain why gravitation is such a weak force, and gravitons from other branes adjacent to our own could provide a potential explanation for dark matter. See brane cosmology.^{[citation needed]}

A theory by Ali and Das adds quantum mechanical corrections (using Bohm trajectories) to general relativistic geodesics. If gravitons are given a small but non-zero mass, it could explain the cosmological constant without need for dark energy and solve the smallness problem.^[13]

Experimental observation

Unambiguous detection of individual gravitons, though not prohibited by any fundamental law, is impossible with any physically reasonable detector.^[14] The reason is the extremely low cross section for the interaction of gravitons with matter. For example, a detector with the mass of Jupiter and 100% efficiency, placed in close orbit around a neutron star, would only be expected to observe one graviton every 10 years, even under the most favorable conditions. It would be impossible to discriminate these events from the background of neutrinos, since the dimensions of the required neutrino shield would ensure collapse into a black hole.^[14]

However, experiments to detect gravitational waves, which may be viewed as coherent states of many gravitons, are underway (e.g., LIGO and VIRGO). Although these experiments cannot detect individual gravitons, they might provide information about certain properties of the graviton.^[15] For example, if gravitational waves were observed to propagate slower than c (the speed of light in a vacuum), that would imply that the graviton has mass (however, gravitational waves must propagate slower than "c" in a region with non-zero mass density if they are to be detectable).^[16] Astronomical observations of the kinematics of galaxies, especially the galaxy rotation problem and modified Newtonian dynamics, might point toward gravitons having non-zero mass.^[17]

Difficulties and outstanding issues

Most theories containing gravitons suffer from severe problems. Attempts to extend the Standard Model or other quantum field theories by adding gravitons run into serious theoretical difficulties at high energies (processes involving energies close to or above the Planck scale) because of infinities arising due to quantum effects (in technical terms, gravitation is nonrenormalizable). Since classical general relativity and quantum mechanics seem to be incompatible at such energies, from a theoretical point of view, this situation is not tenable. One possible solution is to replace particles with strings. String theories are quantum theories of gravity in the sense that they reduce to classical general relativity plus field theory at low energies, but are fully quantum mechanical, contain a graviton, and are believed to be mathematically consistent.^[18]