Metric expansion of space

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The metric expansion of space is the increase of the distance between two distant parts of the universe with time. It is an intrinsic expansion whereby the scale of space itself changes. This is different from other examples of expansions and explosions in that, as far as observations can ascertain, it is a property of the entirety of the universe rather than a phenomenon that can be contained and observed from the outside.

Metric expansion is a key feature of Big Bang cosmology, is modeled mathematically with the FLRW metric, and is a generic property of the universe we inhabit. However, the model is valid only on large scales (roughly the scale of galaxy clusters and above). At smaller scales matter has become bound together under the influence of gravitational attraction and such things do not expand at the metric expansion rate as the universe ages. As such, the only galaxies receding from one another as a result of metric expansion are those separated by cosmologically relevant scales larger than the length scales associated with the gravitational collapse that are possible in the age of the Universe given the matter density and average expansion rate.

At the end of the early universe's inflationary period, all the matter and energy in the universe was set on an inertial trajectory consistent with the equivalence principle and Einstein's general theory of relativity and this is when the precise and regular form of the universe's expansion had its origin (that is, matter in the universe is separating because it was separating in the past due to the inflaton field).
According to measurements, the universe's expansion rate was decelerating until about 5 billion years ago due to the gravitational attraction of the matter content of the universe, after which time the expansion began accelerating. In order to explain the acceleration physicists have postulated the existence of dark energy which appears in the simplest theoretical models as a cosmological constant. According to the simplest extrapolation of the currently-favored cosmological model (known as "ΛCDM"), this acceleration becomes more dominant into the future.

While special relativity constrains objects in the universe from moving faster than light with respect to each other when they are in a local, dynamical relationship, it places no theoretical constraint on the relative motion between two objects that are globally separated and out of causal contact. It is thus possible for two objects to become separated in space by more than the distance light could have travelled, which means that, if the expansion remains constant, the two objects will never come into causal contact. For example, galaxies that are more than approximately 4.5 gigaparsecs away from us are expanding away from us faster than light. We can still see such objects because the universe in the past was expanding more slowly than it is today, so the ancient light being received from these objects is still able to reach us, though if the expansion continues unabated there will never come a time that we will see the light from such objects being produced today (on a so-called "space-like slice of spacetime") and vice-versa because space itself is expanding between Earth and the source faster than any light can be exchanged. Space, in theory, is not infinite.

Because of the high rate of expansion, it is also possible for a distance between two objects to be greater than the value calculated by multiplying the speed of light by the age of the universe. These details are a frequent source of confusion among amateurs and even professional physicists.^[1]

Due to the non-intuitive nature of the subject and what has been described by some as "careless" choices of wording, certain descriptions of the metric expansion of space and the misconceptions to which such descriptions can lead are an ongoing subject of discussion in the realm of pedagogy and communication of scientific concepts.^[2][3][4][5]

Basic concepts and overview

Overview of metrics

To understand the metric expansion of the universe, it is helpful to discuss briefly what a metric is, and how metric expansion works.

Definition of a metric

A metric defines how a distance can be measured between two nearby points in space, in terms of the coordinate system. Coordinate systems locate points in a space (of whatever number of dimensions) by assigning unique positions on a grid, known as coordinates, to each point. The metric is then a formula which describes how displacement through the space of interest can be translated into distances.

Metric for Earth's surface

For example, consider the measurement of distance between two places on the surface of the Earth. This is a simple, familiar example of spherical geometry. Because the surface of the Earth is two-dimensional, points on the surface of the earth can be specified by two coordinates—for
example, the latitude and longitude. Specification of a metric requires that one first specify the coordinates used. In our simple example of the surface of the Earth, we could choose any kind of coordinate system we wish, for example latitude and longitude, or X-Y-Z Cartesian coordinates. Once we have chosen a specific coordinate system, the numerical values of the coordinates of any two points are uniquely determined, and based upon the properties of the space being discussed, the appropriate metric is mathematically established too. On the curved surface of the Earth, we can see this effect in long-haul airline flights where the distance between two points is measured based upon a Great circle, rather than the straight line one might plot on a two-dimensional map of the Earth's surface. In general, such shortest-distance paths are called, "geodesics". In Euclidean geometry, the geodesic is a straight line, while in non-Euclidean geometry such as on the Earth's surface, this is not the case. Indeed even the shortest-distance great circle path is always longer than the Euclidean straight line path which passes through the interior of the Earth. The difference between the straight line path and the shortest-distance great circle path is due to the curvature of the Earth's surface. While there is always an effect due to this curvature, at short distances the effect is small enough to be unnoticeable.

On plane maps, Great circles of the Earth are mostly not shown as straight lines. Indeed, there is a seldom-used map projection, namely the gnomonic projection, where all Great circles are shown as straight lines, but in this projection, the distance scale varies very much in different areas. There is no map projection in which the distance between any two points on Earth, measured along the Great Circle geodesics, is directly proportional to their distance on the map.

Metric tensor

In differential geometry, the backbone mathematics for general relativity, a metric tensor can be defined which precisely characterizes the space being described by explaining the way distances should be measured in every possible direction. General relativity necessarily invokes a metric in four dimensions (one of time, three of space) because, in general, different reference frames will experience different intervals of time and space depending on the inertial frame. This means that the metric tensor in general relativity relates precisely how two events in spacetime are separated. A metric expansion occurs when the metric tensor changes with time (and, specifically, whenever the spatial part of the metric gets larger as time goes forward). This kind of expansion is different from all kinds of expansions and explosions commonly seen in nature in no small part because times and distances are not the same in all reference frames, but are instead subject to change. A useful visualization is to approach the subject rather than objects in a fixed "space" moving apart into "emptiness", as space itself growing between objects without any acceleration of the objects themselves. The space between objects grows or shrinks as the various geodesics converge or diverge.

Because this expansion is caused by relative changes in the distance-defining metric, this expansion (and the resultant movement apart of objects) is not restricted by the speed of light upper bound of special relativity. Two reference frames that are globally separated can be moving apart faster than light without violating special relativity, although whenever two reference frames diverge from each other faster than the speed of light, there will be observable effects associated with such situations including the existence of various cosmological horizons.

Theory and observations suggest that very early in the history of the universe, there was an inflationary phase where the metric changed very rapidly, and that the remaining time-dependence of this metric is what we observe as the so-called Hubble expansion, the moving apart of all gravitationally unbound objects in the universe. The expanding universe is therefore a fundamental feature of the universe we inhabit - a universe fundamentally different from the static universe Albert Einstein first considered when he developed his gravitational theory.

Measuring distances in expanding spaces

In expanding space, proper distances are dynamical quantities which change with time. An easy way to correct for this is to use comoving coordinates which remove this feature and allow for a characterization of different locations in the universe without having to characterize the physics associated with metric expansion. In comoving coordinates, the distances between all objects are fixed and the instantaneous dynamics of matter and light are determined by the normal physics of gravity and electromagnetic radiation. Any time-evolution however must be accounted for by taking into account the Hubble law expansion in the appropriate equations in addition to any other effects that may be operating (gravity, dark energy, or curvature, for example). Cosmological simulations that run through significant fractions of the universe's history therefore must include such effects in order to make applicable predictions for observational cosmology.

Understanding the expansion of the universe

Measurement of expansion and change of rate of expansion

In principle, the expansion of the universe could be measured by taking a standard ruler and measuring the distance between two cosmologically distant points, waiting a certain time, and then measuring the distance again, but in practice, standard rulers are not easy to find on cosmological scales and the time scales over which a measurable expansion would be visible are too great to be observable even by multiple generations of humans. The expansion of space is measured indirectly.
The theory of relativity predicts phenomena associated with the expansion, notably the redshift-versus-distance relationship known as Hubble's Law; functional forms for cosmological distance measurements that differ from what would be expected if space were not expanding; and an observable change in the matter and energy density of the universe seen at different lookback times.

The first measurement of the expansion of space occurred with the creation of the Hubble diagram. Using standard candles with known intrinsic brightness, the expansion of the universe has been measured using redshift to derive Hubble's Constant: H₀ = 67.15 ± 1.2 (km/s)/Mpc. For every million parsecs of distance from the observer, the rate of expansion increases by about 67 kilometers per second.^[6][7][8]

Hubble's Constant is not thought to be constant through time. There are dynamical forces acting on the particles in the universe which affect the expansion rate. It was earlier expected that the Hubble Constant would be decreasing as time went on due to the influence of gravitational interactions in the universe, and thus there is an additional observable quantity in the universe called the deceleration parameter which cosmologists expected to be directly related to the matter density of the universe. Surprisingly, the deceleration parameter was measured by two different groups to be less than zero (actually, consistent with −1) which implied that today Hubble's Constant is increasing as time goes on. Some cosmologists have whimsically called the effect associated with the "accelerating universe" the "cosmic jerk".^[9] The 2011 Nobel Prize in Physics was given for the discovery of this phenomenon.^[10]

Measuring distances in expanding space

Two views of an isometric embedding of part of the visible universe over most of its history, showing how a light ray (red line) can travel an effective distance of 28 billion light years (orange line) in just 13 billion years of cosmological time. Click the images to zoom. (Mathematical details)

At cosmological scales the present universe is geometrically flat, which is to say that the rules of Euclidean geometry associated with Euclid's fifth postulate hold, though in the past spacetime could have been highly curved. In part to accommodate such different geometries, the expansion of the universe is inherently general relativistic; it cannot be modeled with special relativity alone, though such models can be written down, they are at fundamental odds with the observed interaction between matter and spacetime seen in our universe.

The images to the right show two views of spacetime diagrams that show the large-scale geometry of the universe according to the ΛCDM cosmological model. Two of the dimensions of space are omitted, leaving one dimension of space (the dimension that grows as the cone gets larger) and one of time (the dimension that proceeds "up" the cone's surface). The narrow circular end of the diagram corresponds to a cosmological time of 700 million years after the big bang while the wide end is a cosmological time of 18 billion years, where one can see the beginning of the accelerating expansion as a splaying outward of the spacetime, a feature which eventually dominates in this model. The purple grid lines mark off cosmological time at intervals of one billion years from the big bang. The cyan grid lines mark off comoving distance at intervals of one billion light years in the present era (less in the past and more in the future). Note that the circular curling of the surface is an artifact of the embedding with no physical significance and is done purely to make the illustration viewable; space does not actually curl around on itself. (A similar effect can be seen in the tubular shape of the pseudosphere.)

The brown line on the diagram is the worldline of the Earth (or, at earlier times, of the matter which condensed to form the Earth). The yellow line is the worldline of the most distant known quasar. The red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching the Earth in the present day. The orange line shows the present-day distance between the quasar and the Earth, about 28 billion light years, which is, notably, a larger distance than the age of the universe multiplied by the speed of light: ct.

According to the equivalence principle of general relativity, the rules of special relativity are locally valid in small regions of spacetime that are approximately flat. In particular, light always travels locally at the speed c; in our diagram, this means, according to the convention of constructing spacetime diagrams, that light beams always make an angle of 45° with the local grid lines. It does not follow, however, that light travels a distance ct in a time t, as the red worldline illustrates. While it always moves locally at c, its time in transit (about 13 billion years) is not related to the distance traveled in any simple way since the universe expands as the light beam traverses space and time. In fact the distance traveled is inherently ambiguous because of the changing scale of the universe. Nevertheless, we can single out two distances which appear to be physically meaningful: the distance between the Earth and the quasar when the light was emitted, and the distance between them in the present era (taking a slice of the cone along the dimension that we've declared to be the spatial dimension). The former distance is about 4 billion light years, much smaller than ct because the universe expanded as the light traveled the distance, the light had to "run against the treadmill" and therefore went farther than the initial separation between the Earth and the quasar. The latter distance (shown by the orange line) is about 28 billion light years, much larger than ct. If expansion could be instantaneously stopped today, it would take 28 billion years for light to travel between the Earth and the quasar while if the expansion had stopped at the earlier time, it would have taken only 4 billion years.

The light took much longer than 4 billion years to reach us though it was emitted from only 4 billion light years away, and, in fact, the light emitted towards the Earth was actually moving away from the Earth when it was first emitted, in the sense that the metric distance to the Earth increased with cosmological time for the first few billion years of its travel time, and also indicating that the expansion of space between the Earth and the quasar at the early time was faster than the speed of light. None of this surprising behavior originates from a special property of metric expansion, but simply from local principles of special relativity integrated over a curved surface.

Topology of expanding space

A graphical representation of the expansion of the universe with the inflationary epoch represented as the dramatic expansion of the metric seen on the left. This diagram can be confusing because the expansion of space looks like it is happening into an empty "nothingness". However, this is a choice made for convenience of visualization: it is not a part of the physical models which describe the expansion.

Over time, the space that makes up the universe is expanding. The words 'space' and 'universe', sometimes used interchangeably, have distinct meanings in this context. Here 'space' is a mathematical concept that stands for the three-dimensional manifold into which our respective positions are embedded while 'universe' refers to everything that exists including the matter and energy in space, the extra-dimensions that may be wrapped up in various strings, and the time through which various events take place. The expansion of space is in reference to this 3-D manifold only; that is, the description involves no structures such as extra dimensions or an exterior universe.^[11]

The ultimate topology of space is a posteriori—something which in principle must be observed—as there are no constraints that can simply be reasoned out (in other words there can not be any a priori constraints) on how the space in which we live is connected or whether it wraps around on itself as a compact space. Though certain cosmological models such as Gödel's universe even permit bizarre worldlines which intersect with themselves, ultimately the question as to whether we are in something like a "pac-man universe" where if traveling far enough in one direction would allow one to simply end up back in the same place like going all the way around the surface of a balloon (or a planet like the Earth) is an observational question which is constrained as measurable or non-measurable by the universe's global geometry. At present, observations are consistent with the universe being infinite in extent and simply connected, though we are limited in distinguishing between simple and more complicated proposals by cosmological horizons. The universe could be infinite in extent or it could be finite; but the evidence that leads to the inflationary model of the early universe also implies that the "total universe" is much larger than the observable universe, and so any edges or exotic geometries or topologies would not be directly observable as light has not reached scales on which such aspects of the universe, if they exist, are still allowed. For all intents and purposes, it is safe to assume that the universe is infinite in spatial extent, without edge or strange connectedness.^[12]

Regardless of the overall shape of the universe, the question of what the universe is expanding into is one which does not require an answer according to the theories which describe the expansion; the way we define space in our universe in no way requires additional exterior space into which it can expand since an expansion of an infinite expanse can happen without changing the infinite extent of the expanse. All that is certain is that the manifold of space in which we live simply has the property that the distances between objects are getting larger as time goes on. This only implies the simple observational consequences associated with the metric expansion explored below. No "outside" or embedding in hyperspace is required for an expansion to occur. The visualizations often seen of the universe growing as a bubble into nothingness are misleading in that respect. There is no reason to believe there is anything "outside" of the expanding universe into which the universe expands.

Even if the overall spatial extent is infinite and thus the universe can't get any "larger", we still say that space is expanding because, locally, the characteristic distance between objects is increasing. As an infinite space grows, it remains infinite.

Effects of expansion on small scales

The expansion of space is sometimes described as a force which acts to push objects apart. Though this is an accurate description of the effect of the cosmological constant, it is not an accurate picture of the phenomenon of expansion in general. For much of the universe's history the expansion has been due mainly to inertia. The matter in the very early universe was flying apart for unknown reasons (most likely as a result of cosmic inflation) and has simply continued to do so, though at an ever-decreasing rate due to the attractive effect of gravity.

In addition to slowing the overall expansion, gravity causes local clumping of matter into stars and galaxies. Once objects are formed and bound by gravity, they "drop out" of the expansion and do not subsequently expand under the influence of the cosmological metric, there being no force compelling them to do so.

There is no difference between the inertial expansion of the universe and the inertial separation of nearby objects in a vacuum; the former is simply a large-scale extrapolation of the latter.

Once objects are bound by gravity, they no longer recede from each other. Thus, the Andromeda galaxy, which is bound to the Milky Way galaxy, is actually falling towards us and is not expanding away. Within our Local Group of galaxies, the gravitational interactions have changed the inertial patterns of objects such that there is no cosmological expansion taking place. Once one goes beyond the local group, the inertial expansion is measurable, though systematic gravitational effects imply that larger and larger parts of space will eventually fall out of the "Hubble Flow" and end up as bound, non-expanding objects up to the scales of superclusters of galaxies. We can predict such future events by knowing the precise way the Hubble Flow is changing as well as the masses of the objects to which we are being gravitationally pulled. Currently, our Local Group is being gravitationally pulled towards either the Shapley Supercluster or the "Great Attractor" with which, if dark energy were not acting, we would eventually merge and no longer see expand away from us after such a time.

A consequence of metric expansion being due to inertial motion is that a uniform local "explosion" of matter into a vacuum can be locally described by the FLRW geometry, the same geometry which describes the expansion of the universe as a whole and was also the basis for the simpler Milne universe which ignores the effects of gravity. In particular, general relativity predicts that light will move at the speed c with respect to the local motion of the exploding matter, a phenomenon analogous to frame dragging.

The situation changes somewhat with the introduction of dark energy or a cosmological constant. A cosmological constant due to a vacuum energy density has the effect of adding a repulsive force between objects which is proportional (not inversely proportional) to distance. Unlike inertia it actively "pulls" on objects which have clumped together under the influence of gravity, and even on individual atoms. However, this does not cause the objects to grow steadily or to disintegrate; unless they are very weakly bound, they will simply settle into an equilibrium state which is slightly (undetectably) larger than it would otherwise have been. As the universe expands and the matter in it thins, the gravitational attraction decreases (since it is proportional to the density), while the cosmological repulsion increases; thus the ultimate fate of the ΛCDM universe is a near vacuum expanding at an ever increasing rate under the influence of the cosmological constant. However, the only locally visible effect of the accelerating expansion is the disappearance (by runaway redshift) of distant galaxies; gravitationally bound objects like the Milky Way do not expand and the Andromeda galaxy is moving fast enough towards us that it will still merge with the Milky Way in 3 billion years time, and it is also likely that the merged supergalaxy that forms will eventually fall in and merge with the nearby Virgo Cluster. However, galaxies lying farther away from this will recede away at ever-increasing rates of speed and be redshifted out of our range of visibility.

Scale factor

At a fundamental level, the expansion of the universe is a property of spatial measurement on the largest measurable scales of our universe. The distances between cosmologically relevant points increases as time passes leading to observable effects outlined below. This feature of the universe can be characterized by a single parameter that is called the scale factor which is a function of time and a single value for all of space at any instant (if the scale factor were a function of space, this would violate the cosmological principle). By convention, the scale factor is set to be unity at the present time and, because the universe is expanding, is smaller in the past and larger in the future.
Extrapolating back in time with certain cosmological models will yield a moment when the scale factor was zero, our current understanding of cosmology sets this time at 13.798 ± 0.037 billion years ago. If the universe continues to expand forever, the scale factor will approach infinity in the future. In principle, there is no reason that the expansion of the universe must be monotonic and there are models that exist where at some time in the future the scale factor decreases with an attendant contraction of space rather than an expansion.

Other conceptual models of expansion

The expansion of space is often illustrated with conceptual models which show only the size of space at a particular time, leaving the dimension of time implicit.

In the "ant on a rubber rope model" one imagines an ant (idealized as pointlike) crawling at a constant speed on a perfectly elastic rope which is constantly stretching. If we stretch the rope in accordance with the ΛCDM scale factor and think of the ant's speed as the speed of light, then this analogy is numerically accurate—the ant's position over time will match the path of the red line on the embedding diagram above.

In the "rubber sheet model" one replaces the rope with a flat two-dimensional rubber sheet which expands uniformly in all directions. The addition of a second spatial dimension raises the possibility of showing local perturbations of the spatial geometry by local curvature in the sheet.

In the "balloon model" the flat sheet is replaced by a spherical balloon which is inflated from an initial size of zero (representing the big bang). A balloon has positive Gaussian curvature while observations suggest that the real universe is spatially flat, but this inconsistency can be eliminated by making the balloon very large so that it is locally flat to within the limits of observation. This analogy is potentially confusing since it wrongly suggests that the big bang took place at the center of the balloon. In fact points off the surface of the balloon have no meaning, even if they were occupied by the balloon at an earlier time.

Animation of an expanding raisin bread model. As the bread doubles in width (depth and length), the distances between raisins also double.

In the "raisin bread model" one imagines a loaf of raisin bread expanding in the oven. The loaf (space) expands as a whole, but the raisins (gravitationally bound objects) do not expand; they merely grow farther away from each other.

All of these models have the conceptual problem of requiring an outside force acting on the "space" at all times to make it expand. Unlike real cosmological matter, sheets of rubber and loaves of bread are bound together electromagnetically and will not continue to expand on their own after an initial tug.

Theoretical basis and first evidence

Hubble's law

Technically, the metric expansion of space is a feature of many solutions to the Einstein field equations of general relativity, and distance is measured using the Lorentz interval. This explains observations which indicate that galaxies that are more distant from us are receding faster than galaxies that are closer to us (Hubble's law).

Cosmological constant and the Friedmann equations

The first general relativistic models predicted that a universe which was dynamical and contained ordinary gravitational matter would contract rather than expand. Einstein's first proposal for a solution to this problem involved adding a cosmological constant into his theories to balance out the contraction, in order to obtain a static universe solution. But in 1922 Alexander Friedman derived a set of equations known as the Friedmann equations, showing that the universe might expand and presenting the expansion speed in this case.^[13] The observations of Edwin Hubble in 1929 suggested that distant galaxies were all apparently moving away from us, so that many scientists came to accept that the universe was expanding.

Hubble's concerns over the rate of expansion

While the metric expansion of space is implied by Hubble's 1929 observations, Hubble was concerned with the observational implications of the precise value he measured:

"… if redshift are not primarily due to velocity shift … the velocity-distance relation is linear, the distribution of the nebula is uniform, there is no evidence of expansion, no trace of curvature, no restriction of the time scale … and we find ourselves in the presence of one of the principles of nature that is still unknown to us today … whereas, if redshifts are velocity shifts which measure the rate of expansion, the expanding models are definitely inconsistent with the observations that have been made … expanding models are a forced interpretation of the observational results"

— E. Hubble, Ap. J., 84, 517, 1936 ^[14]

"[If the redshifts are a Doppler shift] … the observations as they stand lead to the anomaly of a closed universe, curiously small and dense, and, it may be added, suspiciously young. On the other hand, if redshifts are not Doppler effects, these anomalies disappear and the region observed appears as a small, homogeneous, but insignificant portion of a universe extended indefinitely both in space and time."

— E. Hubble, Monthly Notices of the Royal Astronomical Society, 97, 506, 1937 ^[15]

In fact, Hubble's skepticism about the universe being too small, dense, and young was justified, though it turned out to be an observational error rather than an error of interpretation. Later investigations showed that Hubble had confused distant HII regions for Cepheid variables and the Cepheid variables themselves had been inappropriately lumped together with low-luminosity RR Lyrae stars causing calibration errors that led to a value of the Hubble Constant of approximately 500 km/s/Mpc instead of the true value of approximately 70 km/s/Mpc. The higher value meant that an expanding universe would have an age of 2 billion years (younger than the Age of the Earth) and extrapolating the observed number density of galaxies to a rapidly expanding universe implied a mass density that was too high by a similar factor, enough to force the universe into a peculiar closed geometry which also implied an impending Big Crunch that would occur on a similar time-scale.
After fixing these errors in the 1950s, the new lower values for the Hubble Constant accorded with the expectations of an older universe and the density parameter was found to be fairly close to a geometrically flat universe.^[16]

Inflation as an explanation for the expansion

Until the theoretical developments in the 1980s no one had an explanation for why this seemed to be the case, but with the development of models of cosmic inflation, the expansion of the universe became a general feature resulting from vacuum decay. Accordingly, the question "why is the universe expanding?" is now answered by understanding the details of the inflation decay process which occurred in the first 10⁻³² seconds of the existence of our universe.^[17] During inflation, the metric changed exponentially, causing any volume of space that was smaller than an atom to grow to around 100 million light years across in a time scale similar to the time when inflation occurred (10⁻³² seconds).

The expansion of the universe proceeds in all directions as determined by the Hubble constant. However, the Hubble constant can change in the past and in the future, dependent on the observed value of density parameters (Ω). Before the discovery of dark energy, it was believed that the universe was matter-dominated, and so Ω on this graph corresponds to the ratio of the matter density to the critical density ().

Measuring distance in a metric space

In expanding space, distance is a dynamic quantity which changes with time. There are several different ways of defining distance in cosmology, known as distance measures, but a common method used amongst modern astronomers is comoving distance.
The metric only defines the distance between nearby (so-called "local") points. In order to define the distance between arbitrarily distant points, one must specify both the points and a specific curve (known as a "spacetime interval") connecting them. The distance between the points can then be found by finding the length of this connecting curve through the three dimensions of space. Comoving distance defines this connecting curve to be a curve of constant cosmological time. Operationally, comoving distances cannot be directly measured by a single Earth-bound observer. To determine the distance of distant objects, astronomers generally measure luminosity of standard candles, or the redshift factor 'z' of distant galaxies, and then convert these measurements into distances based on some particular model of space-time, such as the Lambda-CDM model. It is, indeed, by making such observations that it was determined that there is no evidence for any 'slowing down' of the expansion in the current epoch.

Observational evidence

A diagram depicting the expansion of the universe and the appearance of galaxies moving away from a single galaxy. The phenomenon is relative to the observer. Object t1 is a smaller expansion than t2. Each section represents the movement of the red galaxies over the white galaxies for comparison. The blue and green galaxies are markers to show which galaxy is the same one (fixed center point) in the subsequent box. t = time.

Theoretical cosmologists developing models of the universe have drawn upon a small number of reasonable assumptions in their work. These workings have led to models in which the metric expansion of space is a likely feature of the universe. Chief among the underlying principles that result in models including metric expansion as a feature are:

• the Cosmological Principle which demands that the universe looks the same way in all directions (isotropic) and has roughly the same smooth mixture of material (homogeneous).
• the Copernican Principle which demands that no place in the universe is preferred (that is, the universe has no "starting point").

Scientists have tested carefully whether these assumptions are valid and borne out by observation. Observational cosmologists have discovered evidence - very strong in some cases - that supports these assumptions, and as a result, metric expansion of space is considered by cosmologists to be an observed feature on the basis that although we cannot see it directly, scientists have tested the properties of the universe and observation provides compelling confirmation.^[18] Sources of this confidence and confirmation include:

• Hubble demonstrated that all galaxies and distant astronomical objects were moving away from us, as predicted by a universal expansion.^[19] Using the redshift of their electromagnetic spectra to determine the distance and speed of remote objects in space, he showed that all objects are moving away from us, and that their speed is proportional to their distance, a feature of metric expansion. Further studies have since shown the expansion to be highly isotropic and homogeneous, that is, it does not seem to have a special point as a "center", but appears universal and independent of any fixed central point.
• In studies of large-scale structure of the cosmos taken from redshift surveys a so-called "End of Greatness" was discovered at the largest scales of the universe. Until these scales were surveyed, the universe appeared "lumpy" with clumps of galaxy clusters and superclusters and filaments which were anything but isotropic and homogeneous. This lumpiness disappears into a smooth distribution of galaxies at the largest scales.
• The isotropic distribution across the sky of distant gamma-ray bursts and supernovae is another confirmation of the Cosmological Principle.
• The Copernican Principle was not truly tested on a cosmological scale until measurements of the effects of the cosmic microwave background radiation on the dynamics of distant astrophysical systems were made. A group of astronomers at the European Southern Observatory noticed, by measuring the temperature of a distant intergalactic cloud in thermal equilibrium with the cosmic microwave background, that the radiation from the Big Bang was demonstrably warmer at earlier times.^[20] Uniform cooling of the cosmic microwave background over billions of years is strong and direct observational evidence for metric expansion.

Taken together, these phenomena overwhelmingly support models that rely on space expanding through a change in metric. Interestingly, it was not until the discovery in the year 2000 of direct observational evidence for the changing temperature of the cosmic microwave background that more bizarre constructions could be ruled out. Until that time, it was based purely on an assumption that the universe did not behave as one with the Milky Way sitting at the middle of a fixed-metric with a universal explosion of galaxies in all directions (as seen in, for example, an early model proposed by Milne). Yet before this evidence, many rejected the Milne viewpoint based on the mediocrity principle.

The spatial and temporal universality of physical laws was until very recently taken as a fundamental philosophical assumption that is now tested to the observational limits of time and space.

US Solar Makes Up Over Half Of New Generating Capacity

September 8th, 2014 by Joshua S Hill
Original link:  http://cleantechnica.com/2014/09/08/us-solar-makes-half-new-generating-capacity/

The US solar industry has enjoyed a relatively strong quarter in the first half of 2014, despite trade disputes endangering projects currently in the pipeline.

New figures from GTM Research and the Solar Energy Industries Association’s Q2 2014 U.S. Solar Market Insight report show that the US installed 1,133 MW of new solar PV capacity in the second quarter of this year, pushing the cumulative operating capacity for PV and concentrating solar power (CSP) to 15.9 GW.

The most impressive numbers, however, are the shares of new US electric generation capacity across the first half of 2014. Total solar installed capacity for the period represented 53% of all new electricity generating capacity, beating out all competitors by a healthy margin.

“Solar continues to soar, providing more and more homes, businesses, schools and government entities across the United States with clean, reliable and affordable electricity,” said SEIA President and CEO Rhone Resch.

“Solar continues to be a primary source of new electric generation capacity in the US,” added Shayle Kann, Senior Vice President of GTM Research. “With new sources of capital being unlocked, design and engineering innovations reducing system prices, and sales channels rapidly diversifying, the solar market is quickly gaining steam to drive significant growth for the next few years.”


Nothing will quite match the fourth quarter of 2013 in terms of overall installations, given the number of trade disputes and the dissolving of many of the subsidies that pushed such growth, however GTM still contends the last two quarters have been strong ones for the US solar industry. PV installations reached 1,133 MW in the second quarter, and while there were no new CSP installations, during the first quarter of the year the sector celebrated the installation of the largest ever CSP project, the 392 MW Ivanpah project, and the second phase of Genesis Solar’s second 125 MW phase.

California once again topped the charts of installations during the first two quarters of 2014, accounting for more than 50% of installations for the fourth consecutive quarter.


This is definitely a boon for the industry within California, but it does force the industry to rely heavily on California to be the main driver of installations.

The utility PV segment was the main driver of installations over the first half of the year, making up 55% of US solar installations in the second quarter of the year. Utility-scale solar has accounted for more than half of national PV installations for the fifth straight quarter, quadrupling its cumulative size in just two years — growing from 1,784 MW in the first half of 2012 to 7,308 MW


Unsurprisingly then, solar is driving a lot of jobs as well. According to Rhone Resch, the solar industry in the US employs 143,000 people, and funnels nearly $15 billion  year into the national economy.

“This remarkable growth is due in large part to smart and effective public policies, such as the solar Investment Tax Credit (ITC), net energy metering (NEM) and renewable portfolio standards (RPS),” said Resch. “By any measure, these policies are paying huge dividends for both the U.S. economy and the environment, and they should be maintained, if not expanded, given their tremendous success, as well as their importance to America’s future.”

Trade disputes are no doubt going to cast a pall over the third quarter figures, but to what extent is as yet unknown. Chinese manufacturers and suppliers haven’t totally stopped trading with the US, which will undoubtedly help protect a large portion of the US PV pipeline, but just how much of the pipeline will be affected is yet to be seen.

GTM Research and SEIA forecast a total of 6.5 GW of PV to be installed during 2014, up 36% over 2013, but the next few months will prove how likely this figure is.

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Edwin Hubble

From Wikipedia, the free encyclopedia

Edwin Hubble
Born	Edwin Powell Hubble November 20, 1889 Marshfield, Missouri
Died	September 28, 1953 (aged 63) San Marino, California
Residence	United States
Nationality	American
Fields	Astronomy
Institutions	University of Chicago Mount Wilson Observatory
Alma mater	University of Chicago University of Oxford
Known for	Hubble sequence
Influenced	Allan Sandage
Notable awards	Newcomb Cleveland Prize 1924 Bruce Medal 1938 Franklin Medal 1939 Gold Medal of the Royal Astronomical Society 1940 Legion of Merit 1946
Signature

Edwin Powell Hubble (November 20, 1889 – September 28, 1953)^[1] was an American astronomer who played a crucial role in establishing the field of extragalactic astronomy and is generally regarded as one of the most important observational cosmologists of the 20th century. Hubble is known for showing that the recessional velocity of a galaxy increases with its distance from the earth, implying the universe is expanding.^[2] Known as "Hubble's law", this relation had been discovered previously by Georges Lemaître, a Belgian priest/astronomer who published his work in a less visible journal. There is still much controversy surrounding the issue,^[3] and some argue that it should be referred to as "Lemaître's law", although this change has not taken hold in the astronomy community.
Hubble is also known for providing substantial evidence that many objects then classified as "nebulae" were actually galaxies beyond the Milky Way.^[4] American astronomer Vesto Slipher provided the first evidence for this argument almost a decade before.^[5][6]

Hubble supported the Doppler shift interpretation of the observed redshift that had been proposed earlier by Slipher, and that led to the theory of the metric expansion of space.^[7][8] He tended to believe that the frequency of light could, by some so far unknown means, decrease the longer light travels through space.^[9]

Biography

Edwin Hubble was born to Virginia Lee James (1864-1934)^[10] and John Powell Hubble, an insurance executive, in Marshfield, Missouri, and moved to Wheaton, Illinois, in 1900.^[11] In his younger days, he was noted more for his athletic prowess than his intellectual abilities, although he did earn good grades in every subject except for spelling. Edwin was a gifted athlete playing baseball, football, basketball, and he ran track in both high school and college.^[12] He played a variety of positions on the basketball court from center to shooting guard. In fact Hubble even led the University of Chicago ’s basketball team to their first conference title in 1907.^[12] He won seven first places and a third place in a single high school track and field meet in 1906. That year he also set the state high school record for the high jump in Illinois. Another of his personal interests was dry-fly fishing, and he practiced amateur boxing as well.^[13]

His studies at the University of Chicago were concentrated on mathematics and astronomy, which led to a bachelor of science degree in 1910. Hubble also became a member of the Kappa Sigma Fraternity. He spent the three years at The Queen's College, Oxford after earning his bachelors as one of the university's first Rhodes Scholars, initially studying jurisprudence instead of science (as a promise to his dying father),^[14] and later added literature and Spanish,^[14] and earning his master's degree.^[15]

In 1909, Hubble's father moved his family from Chicago to Shelbyville, Kentucky, so that the family could live in a small town, ultimately settling in nearby Louisville. His father died in the winter of 1913, while Edwin was still in England, and in the summer of 1913, Edwin returned to care for his mother, two sisters, and younger brother, as did his brother William. The family moved once more to Everett Avenue, in Louisville's Highlands neighborhood, to accommodate Edwin and William.^[16]
Hubble was also a dutiful son, who despite his intense interest in astronomy since boyhood, surrendered to his father’s request to study law, first at the University of Chicago and later at Oxford, though he managed to take a few math and science courses. After the death of his father in 1913, Edwin returned to the Midwest from Oxford, but did not have the motivation to practice law. So he taught Spanish, physics, and mathematics at the New Albany High School in New Albany, Indiana for a year before he resolved to start over, at the age of 25, to become a professional astronomer. He also coached the boys' basketball team there. After a year of high-school teaching, he entered
graduate school with the help of his former professor from the University of Chicago to study astronomy at the Yerkes Observatory of the University, where he received his PhD in 1917. His dissertation was titled Photographic Investigations of Faint Nebulae.

When Congress declared war on Germany in 1917, Hubble rushed his dissertation for his PhD, volunteering for the United States Army and was assigned to the newly created 86th Division. He rose to the rank of Major and was found fit for overseas duty on July 9, 1918. The 86th Division never saw combat, and after the end of World War One Hubble spent a year in Cambridge, where he renewed his studies of Astronomy.^[17] In 1919, Hubble was offered a staff position in California by George Ellery Hale, the founder and director of the Carnegie Institution's Mount Wilson Observatory, near Pasadena, California, where he remained on the staff until his death. Hubble also served in the U.S. Army at the Aberdeen Proving Ground during World War II. For his work there, he received the Legion of Merit award. Shortly before his death, Mount Palomar's giant 200-inch (5.1 m) reflector Hale Telescope was completed, and Hubble was the first astronomer to use it. Hubble continued his research at the Mount Wilson and Mount Palomar Observatories, where he remained active until his death.

Although Hubble was raised as a Christian, he later became an agnostic.^[18][19]

Hubble experienced a heart attack in July 1949 while on vacation in Colorado. He was taken care of by his wife, Grace Hubble, and continued on a modified diet and work schedule. He died of cerebral thrombosis (a spontaneous blood clot in his brain) on September 28, 1953, in San Marino, California. No funeral was held for him, and his wife never revealed his burial site.^[20][21][22]

Discoveries

The universe goes beyond the Milky Way galaxy

Edwin Hubble's arrival at Mount Wilson, California in 1919 coincided roughly with the completion of the 100-inch (2.5 m) Hooker Telescope, then the world's largest telescope. At that time, the prevailing view of the cosmos was that the universe consisted entirely of the Milky Way Galaxy.
Using the Hooker Telescope at Mt. Wilson, Hubble identified Cepheid variables (a kind of star; see also standard candle) in several spiral nebulae, including the Andromeda Nebula and Triangulum. His observations, made in 1922–1923, proved conclusively that these nebulae were much too distant to be part of the Milky Way and were, in fact, entire galaxies outside our own. This idea had been opposed by many in the astronomy establishment of the time, in particular by the Harvard University-based Harlow Shapley. Despite the opposition, Hubble, then a thirty-five-year-old scientist, had his findings first published in The New York Times on November 23, 1924,^[23] and then more formally presented in the form of a paper at the January 1, 1925 meeting of the American Astronomical Society.^[24] Hubble's findings fundamentally changed the scientific view of the universe. Supporters of Hubble’s expanding universe theory state that Hubble’s discovery of nebulas outside of our galaxy helped pave the way for future astronomers.^[25] Although some of his more renowned colleagues simply scoffed at Hubble's idea of an expanding universe, Hubble ended up publishing his findings on nebulas. This published work earned him an award titled the American Association Prize and five hundred dollars from Burton E. Livingston of the Committee on Awards.^[12]

Hubble also devised the most commonly used system for classifying galaxies, grouping them according to their appearance in photographic images. He arranged the different groups of galaxies in what became known as the Hubble sequence.^[26]

Redshift increases with distance

The 100-inch (2.5 m) Hooker telescope at Mount Wilson Observatory that Hubble used to measure galaxy distances and a value for the rate of expansion of the universe.

Combining his own measurements of galaxy distances based on Henrietta Swan Leavitt's period-luminosity relationship for Cepheids with Vesto Slipher and Milton L. Humason's measurements of the redshifts associated with the galaxies, he discovered a rough proportionality of the objects' distances with their red shifts.^[2] Though there was considerable scatter (now known to be due to peculiar velocities), he was able to plot a trend line from the 46 galaxies and obtained a value for the Hubble Constant of 500 km/s/Mpc, which is much higher than the currently accepted value due to errors in their distance calibrations. In 1929 Hubble formulated the Redshift Distance Law, nowadays termed simply Hubble's law, which, if the redshift is understood to be a measure of recession velocity, is consistent with the solutions of Einstein’s equations of general relativity for a homogeneous, isotropic expanding space. Although concepts underlying an expanding universe were well understood earlier, this statement by Hubble and Humason led to wider-scale acceptance for this view. The law states that the greater the distance between any two galaxies, the greater their relative speed of separation. But two years before, in 1927, Georges Lemaître, a Belgian Catholic priest and physicist, published a paper in an obscure Belgian journal, Annales de la Société Scientifique de Bruxelles. In that paper, he showed that the data collected by Hubble and two other astronomers up to that time was enough to derive a linear velocity-distance relation between the galaxies, and that this supported a model of an expanding universe based on Einstein’s equations for General Relativity.

This discovery was the first observational support for the Big Bang theory which had been proposed by Georges Lemaître in 1927. The observed velocities of distant galaxies, taken together with the cosmological principle, appeared to show that the universe was expanding in a manner consistent with the Friedmann-Lemaître model of general relativity. In 1931 Hubble wrote a letter to the Dutch cosmologist Willem de Sitter expressing his opinion on the theoretical interpretation of the redshift-distance relation:^[27]

Mr. Humason and I are both deeply sensible of your gracious appreciation of the papers on velocities and distances of nebulae. We use the term ‘apparent’ velocities to emphasize the empirical features of the correlation. The interpretation, we feel, should be left to you and the very few others who are competent to discuss the matter with authority.

Today, the "apparent velocities" in question are understood as an increase in proper distance that occurs due to the expansion of space. Light traveling through stretching space will experience a Hubble-type redshift, a mechanism different from the Doppler effect (although the two mechanisms become equivalent descriptions related by a coordinate transformation for nearby galaxies).
In the 1930s, Hubble was involved in determining the distribution of galaxies and spatial curvature.
These data seemed to indicate that the universe was flat and homogeneous, but there was a deviation from flatness at large redshifts. According to Allan Sandage,

Hubble believed that his count data gave a more reasonable result concerning spatial curvature if the redshift correction was made assuming no recession. To the very end of his writings he maintained this position, favouring (or at the very least keeping open) the model where no true expansion exists, and therefore that the redshift "represents a hitherto unrecognized principle of nature."^[28]

There were methodological problems with Hubble's survey technique that showed a deviation from flatness at large redshifts. In particular, the technique did not account for changes in luminosity of galaxies due to galaxy evolution. Earlier, in 1917, Albert Einstein had found that his newly developed theory of general relativity indicated that the universe must be either expanding or contracting.
Unable to believe what his own equations were telling him, Einstein introduced a cosmological constant (a "fudge factor") to the equations to avoid this "problem". When Einstein learned of Hubble's redshifts, he immediately realized that the expansion predicted by General Relativity must be real, and in later life he said that changing his equations was "the biggest blunder of [his] life." In fact, Einstein apparently once visited Hubble and tried to convince him that the universe was expanding.^[29]

Other discoveries

Hubble discovered the asteroid 1373 Cincinnati on August 30, 1935. He also wrote The Observational Approach to Cosmology and The Realm of the Nebulae approximately during this time.^[30]

No Nobel Prize

Hubble spent much of the later part of his career attempting to have astronomy considered an area of physics, instead of being its own science. He did this largely so that astronomers—including himself—could be recognized by the Nobel Prize Committee for their valuable contributions to astrophysics. This campaign was unsuccessful in Hubble's lifetime, but shortly after his death, the Nobel Prize Committee decided that astronomical work would be eligible for the physics prize.^[12] However, the prize is not one that can be awarded posthumously.

Stamp

On March 6, 2008, the United States Postal Service released a 41-cent stamp honoring Hubble on a sheet titled "American Scientists" designed by artist Victor Stabin.^[21] His citation reads:

Often called a "pioneer of the distant stars," astronomer Edwin Hubble (1889–1953) played a pivotal role in deciphering the vast and complex nature of the universe. His meticulous studies of spiral nebulae proved the existence of galaxies other than our own Milky Way. Had he not died suddenly in 1953, Hubble would have won that year's Nobel Prize in Physics.

The other scientists on the "American Scientists" sheet include Gerty Cori, biochemist; Linus Pauling, chemist, and John Bardeen, physicist.

Honors

Awards

• Newcomb Cleveland Prize in 1924;
• Bruce Medal in 1938;
• Franklin Medal in 1939;
• Gold Medal of the Royal Astronomical Society in 1940;
• Legion of Merit for outstanding contribution to ballistics research in 1946.

Named after him

• Asteroid 2069 Hubble;
• The crater Hubble on the Moon;
• Orbiting Hubble Space Telescope;
• Edwin P. Hubble Planetarium, located in the Edward R. Murrow High School, Brooklyn, NY.;
• Edwin Hubble Highway, the stretch of Interstate 44 passing through his birthplace of Marshfield, Missouri;
• Hall of Famous Missourians 2003;
• 2008 "American Scientists" US stamp series, $0.41.

• The Edwin P. Hubble Medal of Initiative is awarded annually by the city of Marshfield, Missouri — Hubble's birthplace.
• Hubble Middle School in Wheaton, Illinois, was renamed for Edwin Hubble when Wheaton Central High School was converted to a middle school in the fall of 1992.

In Popular Culture

The play "Creation's Birthday", written by Cornell physicist Hasan Padamsee, tells Hubble's life story.^[31] A famous quote by Edwin Hubble goes: "Equipped with his five senses man explores the universe around him and calls the adventure science".^[32]