Introduction to general relativity

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High-precision test of general relativity by the Cassini space probe (artist's impression): radio signals sent between the Earth and the probe (green wave) are delayed by the warping of spacetime (blue lines) due to the Sun's mass.

General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915. According to general relativity, the observed gravitational effect between masses results from their warping of spacetime.

By the beginning of the 20th century, Newton's law of universal gravitation had been accepted for more than two hundred years as a valid description of the gravitational force between masses. In Newton's model, gravity is the result of an attractive force between massive objects. Although even Newton was troubled by the unknown nature of that force,^[1] the basic framework was extremely successful at describing motion.

Experiments and observations show that Einstein's description of gravitation accounts for several effects that are unexplained by Newton's law, such as minute anomalies in the orbits of Mercury and other planets. General relativity also predicts novel effects of gravity, such as gravitational waves, gravitational lensing and an effect of gravity on time known as gravitational time dilation. Many of these predictions have been confirmed by experiment, while others are the subject of ongoing research. For example, although there is indirect evidence for gravitational waves, direct evidence of their existence is still being sought by several teams of scientists in experiments such as the LIGO and GEO600 projects.

General relativity has developed into an essential tool in modern astrophysics. It provides the foundation for the current understanding of black holes, regions of space where the gravitational effect is so strong that even light cannot escape. Their strong gravity is thought to be responsible for the intense radiation emitted by certain types of astronomical objects (such as active galactic nuclei or microquasars). General relativity is also part of the framework of the standard Big Bang model of cosmology.

Although general relativity is not the only relativistic theory of gravity, it is the simplest such theory that is consistent with the experimental data. Nevertheless, a number of open questions remain, the most fundamental of which is how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity.

From special to general relativity

Albert Einstein, pictured here in 1921, developed the theories of special and general relativity.

In September 1905, Albert Einstein published his theory of special relativity, which reconciles Newton's laws of motion with electrodynamics (the interaction between objects with electric charge). Special relativity introduced a new framework for all of physics by proposing new concepts of space and time. Some then-accepted physical theories were inconsistent with that framework; a key example was Newton's theory of gravity, which describes the mutual attraction experienced by bodies due to their mass.

Several physicists, including Einstein, searched for a theory that would reconcile Newton's law of gravity and special relativity. Only Einstein's theory proved to be consistent with experiments and observations. To understand the theory's basic ideas, it is instructive to follow Einstein's thinking between 1907 and 1915, from his simple thought experiment involving an observer in free fall to his fully geometric theory of gravity.^[2]

Equivalence principle

A person in a free-falling elevator experiences weightlessness and objects either float motionless or drift at constant speed. Since everything in the elevator is falling together, no gravitational effect can be observed. In this way, the experiences of an observer in free fall are indistinguishable from those of an observer in deep space, far from any significant source of gravity. Such observers are the privileged ("inertial") observers Einstein described in his theory of special relativity: observers for whom light travels along straight lines at constant speed.^[3]
Einstein hypothesized that the similar experiences of weightless observers and inertial observers in special relativity represented a fundamental property of gravity, and he made this the cornerstone of his theory of general relativity, formalized in his equivalence principle. Roughly speaking, the principle states that a person in a free-falling elevator cannot tell that they are in free fall. Every experiment in such a free-falling environment has the same results as it would for an observer at rest or moving uniformly in deep space, far from all sources of gravity.^[4]

Gravity and acceleration

Ball falling to the floor in an accelerating rocket (left) and on Earth (right).

Most effects of gravity vanish in free fall, but effects that seem the same as those of gravity can be produced by an accelerated frame of reference. An observer in a closed room cannot tell which of the following is true:

• Objects are falling to the floor because the room is resting on the surface of the Earth and the objects are being pulled down by gravity.
• Objects are falling to the floor because the room is aboard a rocket in space, which is accelerating at 9.81 m/s² and is far from any source of gravity. The objects are being pulled towards the floor by the same "inertial force" that presses the driver of an accelerating car into the back of his seat.

Conversely, any effect observed in an accelerated reference frame should also be observed in a gravitational field of corresponding strength. This principle allowed Einstein to predict several novel effects of gravity in 1907, as explained in the next section.

An observer in an accelerated reference frame must introduce what physicists call fictitious forces to account for the acceleration experienced by himself and objects around him. One example, the force pressing the driver of an accelerating car into his or her seat, has already been mentioned; another is the force you can feel pulling your arms up and out if you attempt to spin around like a top. Einstein's master insight was that the constant, familiar pull of the Earth's gravitational field is fundamentally the same as these fictitious forces.^[5] The apparent magnitude of the fictitious forces always appears to be proportional to the mass of any object on which they act - for instance, the driver's seat exerts just enough force to accelerate the driver at the same rate as the car. By analogy, Einstein proposed that an object in a gravitational field should feel a gravitational force proportional to its mass, as embodied in Newton's law of gravitation.^[6]

Physical consequences

In 1907, Einstein was still eight years away from completing the general theory of relativity. Nonetheless, he was able to make a number of novel, testable predictions that were based on his starting point for developing his new theory: the equivalence principle.^[7]

The gravitational redshift of a light wave as it moves upwards against a gravitational field (caused by the yellow star below).

The first new effect is the gravitational frequency shift of light. Consider two observers aboard an accelerating rocket-ship. Aboard such a ship, there is a natural concept of "up" and "down": the direction in which the ship accelerates is "up", and unattached objects accelerate in the opposite direction, falling "downward". Assume that one of the observers is "higher up" than the other. When the lower observer sends a light signal to the higher observer, the acceleration causes the light to be red-shifted, as may be calculated from special relativity; the second observer will measure a lower frequency for the light than the first. Conversely, light sent from the higher observer to the lower is blue-shifted, that is, shifted towards higher frequencies.^[8] Einstein argued that such frequency shifts must also be observed in a gravitational field. This is illustrated in the figure at left, which shows a light wave that is gradually red-shifted as it works its way upwards against the gravitational acceleration. This effect has been confirmed experimentally, as described below.

This gravitational frequency shift corresponds to a gravitational time dilation: Since the "higher" observer measures the same light wave to have a lower frequency than the "lower" observer, time must be passing faster for the higher observer. Thus, time runs more slowly for observers who are lower in a gravitational field.

It is important to stress that, for each observer, there are no observable changes of the flow of time for events or processes that are at rest in his or her reference frame. Five-minute-eggs as timed by each observer's clock have the same consistency; as one year passes on each clock, each observer ages by that amount; each clock, in short, is in perfect agreement with all processes happening in its immediate vicinity. It is only when the clocks are compared between separate observers that one can notice that time runs more slowly for the lower observer than for the higher.^[9] This effect is minute, but it too has been confirmed experimentally in multiple experiments, as described below.

In a similar way, Einstein predicted the gravitational deflection of light: in a gravitational field, light is deflected downward. Quantitatively, his results were off by a factor of two; the correct derivation requires a more complete formulation of the theory of general relativity, not just the equivalence principle.^[10]

Tidal effects

Two bodies falling towards the center of the Earth accelerate towards each other as they fall.

The equivalence between gravitational and inertial effects does not constitute a complete theory of gravity. When it comes to explaining gravity near our own location on the Earth's surface, noting that our reference frame is not in free fall, so that fictitious forces are to be expected, provides a suitable explanation. But a freely falling reference frame on one side of the Earth cannot explain why the people on the opposite side of the Earth experience a gravitational pull in the opposite direction.

A more basic manifestation of the same effect involves two bodies that are falling side by side towards the Earth. In a reference frame that is in free fall alongside these bodies, they appear to hover weightlessly – but not exactly so. These bodies are not falling in precisely the same direction, but towards a single point in space: namely, the Earth's center of gravity. Consequently, there is a component of each body's motion towards the other (see the figure). In a small environment such as a freely falling lift, this relative acceleration is minuscule, while for skydivers on opposite sides of the Earth, the effect is large. Such differences in force are also responsible for the tides in the Earth's oceans, so the term "tidal effect" is used for this phenomenon.

The equivalence between inertia and gravity cannot explain tidal effects – it cannot explain variations in the gravitational field.^[11] For that, a theory is needed which describes the way that matter (such as the large mass of the Earth) affects the inertial environment around it.

From acceleration to geometry

In exploring the equivalence of gravity and acceleration as well as the role of tidal forces, Einstein discovered several analogies with the geometry of surfaces. An example is the transition from an inertial reference frame (in which free particles coast along straight paths at constant speeds) to a rotating reference frame (in which extra terms corresponding to fictitious forces have to be introduced in order to explain particle motion): this is analogous to the transition from a Cartesian coordinate system (in which the coordinate lines are straight lines) to a curved coordinate system (where coordinate lines need not be straight).

A deeper analogy relates tidal forces with a property of surfaces called curvature. For gravitational fields, the absence or presence of tidal forces determines whether or not the influence of gravity can be eliminated by choosing a freely falling reference frame. Similarly, the absence or presence of curvature determines whether or not a surface is equivalent to a plane. In the summer of 1912, inspired by these analogies, Einstein searched for a geometric formulation of gravity.^[12]

The elementary objects of geometry – points, lines, triangles – are traditionally defined in three-dimensional space or on two-dimensional surfaces. In 1907, Hermann Minkowski, Einstein's former mathematics professor at the Swiss Federal Polytechnic, introduced a geometric formulation of Einstein's special theory of relativity where the geometry included not only space but also time. The basic entity of this new geometry is four-dimensional spacetime. The orbits of moving bodies are curves in spacetime; the orbits of bodies moving at constant speed without changing direction correspond to straight lines.^[13]

For surfaces, the generalization from the geometry of a plane – a flat surface – to that of a general curved surface had been described in the early 19th century by Carl Friedrich Gauss. This description had in turn been generalized to higher-dimensional spaces in a mathematical formalism introduced by Bernhard Riemann in the 1850s. With the help of Riemannian geometry, Einstein formulated a geometric description of gravity in which Minkowski's spacetime is replaced by distorted, curved spacetime, just as curved surfaces are a generalization of ordinary plane surfaces.^[14]

After he had realized the validity of this geometric analogy, it took Einstein a further three years to find the missing cornerstone of his theory: the equations describing how matter influences spacetime's curvature. Having formulated what are now known as Einstein's equations (or, more precisely, his field equations of gravity), he presented his new theory of gravity at several sessions of the Prussian Academy of Sciences in late 1915, culminating in his final presentation on November 25, 1915.^[15]

Geometry and gravitation

Paraphrasing John Wheeler, Einstein's geometric theory of gravity can be summarized thus: spacetime tells matter how to move; matter tells spacetime how to curve.^[16] What this means is addressed in the following three sections, which explore the motion of so-called test particles, examine which properties of matter serve as a source for gravity, and, finally, introduce Einstein's equations, which relate these matter properties to the curvature of spacetime.

Probing the gravitational field

Converging geodesics: two lines of longitude (green) that start out in parallel at the equator (red) but converge to meet at the pole.

In order to map a body's gravitational influence, it is useful to think about what physicists call probe or test particles: particles that are influenced by gravity, but are so small and light that we can neglect their own gravitational effect. In the absence of gravity and other external forces, a test particle moves along a straight line at a constant speed. In the language of spacetime, this is equivalent to saying that such test particles move along straight world lines in spacetime. In the presence of gravity, spacetime is non-Euclidean, or curved, and in curved spacetime straight world lines may not exist. Instead, test particles move along lines called geodesics, which are "as straight as possible", that is, they follow the shortest path between starting and ending points, taking the curvature into consideration.

A simple analogy is the following: In geodesy, the science of measuring Earth's size and shape, a geodesic (from Greek "geo", Earth, and "daiein", to divide) is the shortest route between two points on the Earth's surface. Approximately, such a route is a segment of a great circle, such as a line of longitude or the equator. These paths are certainly not straight, simply because they must follow the curvature of the Earth's surface. But they are as straight as is possible subject to this constraint.

The properties of geodesics differ from those of straight lines. For example, on a plane, parallel lines never meet, but this is not so for geodesics on the surface of the Earth: for example, lines of longitude are parallel at the equator, but intersect at the poles. Analogously, the world lines of test particles in free fall are spacetime geodesics, the straightest possible lines in spacetime. But still there are crucial differences between them and the truly straight lines that can be traced out in the gravity-free spacetime of special relativity. In special relativity, parallel geodesics remain parallel. In a gravitational field with tidal effects, this will not, in general, be the case. If, for example, two bodies are initially at rest relative to each other, but are then dropped in the Earth's gravitational field, they will move towards each other as they fall towards the Earth's center.^[17]

Compared with planets and other astronomical bodies, the objects of everyday life (people, cars, houses, even mountains) have little mass. Where such objects are concerned, the laws governing the behavior of test particles are sufficient to describe what happens. Notably, in order to deflect a test particle from its geodesic path, an external force must be applied. A person sitting on a chair is trying to follow a geodesic, that is, to fall freely towards the center of the Earth. But the chair applies an external upwards force preventing the person from falling. In this way, general relativity explains the daily experience of gravity on the surface of the Earth not as the downwards pull of a gravitational force, but as the upwards push of external forces. These forces deflect all bodies resting on the Earth's surface from the geodesics they would otherwise follow.^[18] For matter objects whose own gravitational influence cannot be neglected, the laws of motion are somewhat more complicated than for test particles, although it remains true that spacetime tells matter how to move.^[19]

Sources of gravity

In Newton's description of gravity, the gravitational force is caused by matter. More precisely, it is caused by a specific property of material objects: their mass. In Einstein's theory and related theories of gravitation, curvature at every point in spacetime is also caused by whatever matter is present. Here, too, mass is a key property in determining the gravitational influence of matter. But in a relativistic theory of gravity, mass cannot be the only source of gravity. Relativity links mass with energy, and energy with momentum.

The equivalence between mass and energy, as expressed by the formula E = mc², is the most famous consequence of special relativity. In relativity, mass and energy are two different ways of describing one physical quantity. If a physical system has energy, it also has the corresponding mass, and vice versa. In particular, all properties of a body that are associated with energy, such as its temperature or the binding energy of systems such as nuclei or molecules, contribute to that body's mass, and hence act as sources of gravity.^[20]

In special relativity, energy is closely connected to momentum. Just as space and time are, in that theory, different aspects of a more comprehensive entity called spacetime, energy and momentum are merely different aspects of a unified, four-dimensional quantity that physicists call four-momentum. In consequence, if energy is a source of gravity, momentum must be a source as well. The same is true for quantities that are directly related to energy and momentum, namely internal pressure and tension. Taken together, in general relativity it is mass, energy, momentum, pressure and tension that serve as sources of gravity: they are how matter tells spacetime how to curve. In the theory's mathematical formulation, all these quantities are but aspects of a more general physical quantity called the energy–momentum tensor.^[21]

Einstein's equations

Einstein's equations are the centerpiece of general relativity. They provide a precise formulation of the relationship between spacetime geometry and the properties of matter, using the language of mathematics. More concretely, they are formulated using the concepts of Riemannian geometry, in which the geometric properties of a space (or a spacetime) are described by a quantity called a metric. The metric encodes the information needed to compute the fundamental geometric notions of distance and angle in a curved space (or spacetime).

Distances, at different latitudes, corresponding to 30 degrees difference in longitude.

A spherical surface like that of the Earth provides a simple example. The location of any point on the surface can be described by two coordinates: the geographic latitude and longitude. Unlike the Cartesian coordinates of the plane, coordinate differences are not the same as distances on the surface, as shown in the diagram on the right: for someone at the equator, moving 30 degrees of longitude westward (magenta line) corresponds to a distance of roughly 3,300 kilometers (2,100 mi). On the other hand, someone at a latitude of 55 degrees, moving 30 degrees of longitude westward (blue line) covers a distance of merely 1,900 kilometers (1,200 mi). Coordinates therefore do not provide enough information to describe the geometry of a spherical surface, or indeed the geometry of any more complicated space or spacetime. That information is precisely what is encoded in the metric, which is a function defined at each point of the surface (or space, or spacetime) and relates coordinate differences to differences in distance. All other quantities that are of interest in geometry, such as the length of any given curve, or the angle at which two curves meet, can be computed from this metric function.^[22]

The metric function and its rate of change from point to point can be used to define a geometrical quantity called the Riemann curvature tensor, which describes exactly how the space or spacetime is curved at each point. In general relativity, the metric and the Riemann curvature tensor are quantities defined at each point in spacetime. As has already been mentioned, the matter content of the spacetime defines another quantity, the energy–momentum tensor T, and the principle that "spacetime tells matter how to move, and matter tells spacetime how to curve" means that these quantities must be related to each other. Einstein formulated this relation by using the Riemann curvature tensor and the metric to define another geometrical quantity G, now called the Einstein tensor, which describes some aspects of the way spacetime is curved. Einstein's equation then states that

${\mathbf {G}}={\frac {8\pi G}{c^{4}}}{\mathbf {T}},$

i.e. up to a constant multiple, the quantity G (which measures curvature) is equated with the quantity T (which measures matter content). The constants involved in this equation reflect the different theories that went into its making: π is one of the basic constants of geometry, G is the gravitational constant that is already present in Newtonian gravity, and c is the speed of light, the key constant in special relativity.

This equation is often referred to in the plural as Einstein's equations, since the quantities G and T are each determined by several functions of the coordinates of spacetime, and the equations equate each of these component functions.^[23] A solution of these equations describes a particular geometry of spacetime; for example, the Schwarzschild solution describes the geometry around a spherical, non-rotating mass such as a star or a black hole, whereas the Kerr solution describes a rotating black hole. Still other solutions can describe a gravitational wave or, in the case of the Friedmann–Lemaître–Robertson–Walker solution, an expanding universe. The simplest solution is the uncurved Minkowski spacetime, the spacetime described by special relativity.^[24]

Experiments

No scientific theory is apodictically true; each is a model that must be checked by experiment. Newton's law of gravity was accepted because it accounted for the motion of planets and moons in the solar system with considerable accuracy. As the precision of experimental measurements gradually improved, some discrepancies with Newton's predictions were observed, and these were accounted for in the general theory of relativity. Similarly, the predictions of general relativity must also be checked with experiment, and Einstein himself devised three tests now known as the classical tests of the theory:

Newtonian (red) vs. Einsteinian orbit (blue) of a single planet orbiting a spherical star. (Click on the image for animation.)

• Newtonian gravity predicts that the orbit which a single planet traces around a perfectly spherical star should be an ellipse. Einstein's theory predicts a more complicated curve: the planet behaves as if it were travelling around an ellipse, but at the same time, the ellipse as a whole is rotating slowly around the star. In the diagram on the right, the ellipse predicted by Newtonian gravity is shown in red, and part of the orbit predicted by Einstein in blue. For a planet orbiting the Sun, this deviation from Newton's orbits is known as the anomalous perihelion shift. The first measurement of this effect, for the planet Mercury, dates back to 1859. The most accurate results for Mercury and for other planets to date are based on measurements which were undertaken between 1966 and 1990, using radio telescopes.^[25] General relativity predicts the correct anomalous perihelion shift for all planets where this can be measured accurately (Mercury, Venus and the Earth).
• According to general relativity, light does not travel along straight lines when it propagates in a gravitational field. Instead, it is deflected in the presence of massive bodies. In particular, starlight is deflected as it passes near the Sun, leading to apparent shifts of up 1.75 arc seconds in the stars' positions in the sky (an arc second is equal to 1/3600 of a degree). In the framework of Newtonian gravity, a heuristic argument can be made that leads to light deflection by half that amount. The different predictions can be tested by observing stars that are close to the Sun during a solar eclipse. In this way, a British expedition to West Africa in 1919, directed by Arthur Eddington, confirmed that Einstein's prediction was correct, and the Newtonian predictions wrong, via observation of the May 1919 eclipse. Eddington's results were not very accurate; subsequent observations of the deflection of the light of distant quasars by the Sun, which utilize highly accurate techniques of radio astronomy, have confirmed Eddington's results with significantly better precision (the first such measurements date from 1967, the most recent comprehensive analysis from 2004).^[26]
• Gravitational redshift was first measured in a laboratory setting in 1959 by Pound and Rebka. It is also seen in astrophysical measurements, notably for light escaping the white dwarf Sirius B. The related gravitational time dilation effect has been measured by transporting atomic clocks to altitudes of between tens and tens of thousands of kilometers (first by Hafele and Keating in 1971; most accurately to date by Gravity Probe A launched in 1976).^[27]

Of these tests, only the perihelion advance of Mercury was known prior to Einstein's final publication of general relativity in 1916. The subsequent experimental confirmation of his other predictions, especially the first measurements of the deflection of light by the sun in 1919, catapulted Einstein to international stardom.^[28] These three experiments justified adopting general relativity over Newton's theory and, incidentally, over a number of alternatives to general relativity that had been proposed.

Gravity Probe B with solar panels folded.

Further tests of general relativity include precision measurements of the Shapiro effect or gravitational time delay for light, most recently in 2002 by the Cassini space probe. One set of tests focuses on effects predicted by general relativity for the behavior of gyroscopes travelling through space. One of these effects, geodetic precession, has been tested with the Lunar Laser Ranging Experiment (high-precision measurements of the orbit of the Moon). Another, which is related to rotating masses, is called frame-dragging. The geodetic and frame-dragging effects were both tested by the Gravity Probe B satellite experiment launched in 2004, with results confirming relativity to within 0.5% and 15%, respectively, as of December 2008.^[29]

By cosmic standards, gravity throughout the solar system is weak. Since the differences between the predictions of Einstein's and Newton's theories are most pronounced when gravity is strong, physicists have long been interested in testing various relativistic effects in a setting with comparatively strong gravitational fields. This has become possible thanks to precision observations of binary pulsars. In such a star system, two highly compact neutron stars orbit each other. At least one of them is a pulsar – an astronomical object that emits a tight beam of radiowaves. These beams strike the Earth at very regular intervals, similarly to the way that the rotating beam of a lighthouse means that an observer sees the lighthouse blink, and can be observed as a highly regular series of pulses. General relativity predicts specific deviations from the regularity of these radio pulses. For instance, at times when the radio waves pass close to the other neutron star, they should be deflected by the star's gravitational field. The observed pulse patterns are impressively close to those predicted by general relativity.^[30]

One particular set of observations is related to eminently useful practical applications, namely to satellite navigation systems such as the Global Positioning System that are used both for precise positioning and timekeeping. Such systems rely on two sets of atomic clocks: clocks aboard satellites orbiting the Earth, and reference clocks stationed on the Earth's surface. General relativity predicts that these two sets of clocks should tick at slightly different rates, due to their different motions (an effect already predicted by special relativity) and their different positions within the Earth's gravitational field. In order to ensure the system's accuracy, the satellite clocks are either slowed down by a relativistic factor, or that same factor is made part of the evaluation algorithm. In turn, tests of the system's accuracy (especially the very thorough measurements that are part of the definition of universal coordinated time) are testament to the validity of the relativistic predictions.^[31]

A number of other tests have probed the validity of various versions of the equivalence principle; strictly speaking, all measurements of gravitational time dilation are tests of the weak version of that principle, not of general relativity itself. So far, general relativity has passed all observational tests.^[32]

Astrophysical applications

Models based on general relativity play an important role in astrophysics; the success of these models is further testament to the theory's validity.

Gravitational lensing

Einstein cross: four images of the same astronomical object, produced by a gravitational lens.

Since light is deflected in a gravitational field, it is possible for the light of a distant object to reach an observer along two or more paths. For instance, light of a very distant object such as a quasar can pass along one side of a massive galaxy and be deflected slightly so as to reach an observer on Earth, while light passing along the opposite side of that same galaxy is deflected as well, reaching the same observer from a slightly different direction. As a result, that particular observer will see one astronomical object in two different places in the night sky. This kind of focussing is well-known when it comes to optical lenses, and hence the corresponding gravitational effect is called gravitational lensing.^[33]

Observational astronomy uses lensing effects as an important tool to infer properties of the lensing object. Even in cases where that object is not directly visible, the shape of a lensed image provides information about the mass distribution responsible for the light deflection. In particular, gravitational lensing provides one way to measure the distribution of dark matter, which does not give off light and can be observed only by its gravitational effects. One particularly interesting application are large-scale observations, where the lensing masses are spread out over a significant fraction of the observable universe, and can be used to obtain information about the large-scale properties and evolution of our cosmos.^[34]

Gravitational waves

Gravitational waves, a direct consequence of Einstein's theory, are distortions of geometry that propagate at the speed of light, and can be thought of as ripples in spacetime. They should not be confused with the gravity waves of fluid dynamics, which are a different concept.

Indirectly, the effect of gravitational waves has been detected in observations of specific binary stars. Such pairs of stars orbit each other and, as they do so, gradually lose energy by emitting gravitational waves. For ordinary stars like the Sun, this energy loss would be too small to be detectable, but this energy loss was observed in 1974 in a binary pulsar called PSR1913+16. In such a system, one of the orbiting stars is a pulsar. This has two consequences: a pulsar is an extremely dense object known as a neutron star, for which gravitational wave emission is much stronger than for ordinary stars. Also, a pulsar emits a narrow beam of electromagnetic radiation from its magnetic poles. As the pulsar rotates, its beam sweeps over the Earth, where it is seen as a regular series of radio pulses, just as a ship at sea observes regular flashes of light from the rotating light in a lighthouse. This regular pattern of radio pulses functions as a highly accurate "clock". It can be used to time the double star's orbital period, and it reacts sensitively to distortions of spacetime in its immediate neighborhood.

The discoverers of PSR1913+16, Russell Hulse and Joseph Taylor, were awarded the Nobel Prize in Physics in 1993. Since then, several other binary pulsars have been found. The most useful are those in which both stars are pulsars, since they provide the most accurate tests of general relativity.^[35]

Currently, one major goal of research in relativity is the direct detection of gravitational waves. To this end, a number of land-based gravitational wave detectors are in operation, and a mission to launch a space-based detector, LISA, is currently under development, with a precursor mission (LISA Pathfinder) due for launch in 2015. If gravitational waves are detected, they could be used to obtain information about compact objects such as neutron stars and black holes, and also to probe the state of the early universe fractions of a second after the Big Bang.^[36]

Black holes

Black hole-powered jet emanating from the central region of the galaxy M87.

When mass is concentrated into a sufficiently compact region of space, general relativity predicts the formation of a black hole – a region of space with a gravitational effect so strong that not even light can escape. Certain types of black holes are thought to be the final state in the evolution of massive stars. On the other hand, supermassive black holes with the mass of millions or billions of Suns are assumed to reside in the cores of most galaxies, and they play a key role in current models of how galaxies have formed over the past billions of years.^[37]

Matter falling onto a compact object is one of the most efficient mechanisms for releasing energy in the form of radiation, and matter falling onto black holes is thought to be responsible for some of the brightest astronomical phenomena imaginable. Notable examples of great interest to astronomers are quasars and other types of active galactic nuclei. Under the right conditions, falling matter accumulating around a black hole can lead to the formation of jets, in which focused beams of matter are flung away into space at speeds near that of light.^[38]

There are several properties that make black holes most promising sources of gravitational waves. One reason is that black holes are the most compact objects that can orbit each other as part of a binary system; as a result, the gravitational waves emitted by such a system are especially strong. Another reason follows from what are called black-hole uniqueness theorems: over time, black holes retain only a minimal set of distinguishing features (these theorems have become known as "no-hair" theorems, since different hairstyles are a crucial part of what gives different people their different appearances). For instance, in the long term, the collapse of a hypothetical matter cube will not result in a cube-shaped black hole. Instead, the resulting black hole will be indistinguishable from a black hole formed by the collapse of a spherical mass, but with one important difference: in its transition to a spherical shape, the black hole formed by the collapse of a cube will emit gravitational waves.^[39]

Cosmology

An image, created using data from the WMAP satellite telescope, of the radiation emitted no more than a few hundred thousand years after the Big Bang.

One of the most important aspects of general relativity is that it can be applied to the universe as a whole. A key point is that, on large scales, our universe appears to be constructed along very simple lines: all current observations suggest that, on average, the structure of the cosmos should be approximately the same, regardless of an observer's location or direction of observation: the universe is approximately homogeneous and isotropic. Such comparatively simple universes can be described by simple solutions of Einstein's equations. The current cosmological models of the universe are obtained by combining these simple solutions to general relativity with theories describing the properties of the universe's matter content, namely thermodynamics, nuclear- and particle physics. According to these models, our present universe emerged from an extremely dense high-temperature state – the Big Bang – roughly 14 billion years ago and has been expanding ever since.^[40]

Einstein's equations can be generalized by adding a term called the cosmological constant. When this term is present, empty space itself acts as a source of attractive (or, less commonly, repulsive) gravity. Einstein originally introduced this term in his pioneering 1917 paper on cosmology, with a very specific motivation: contemporary cosmological thought held the universe to be static, and the additional term was required for constructing static model universes within the framework of general relativity. When it became apparent that the universe is not static, but expanding, Einstein was quick to discard this additional term. Since the end of the 1990s, however, astronomical evidence indicating an accelerating expansion consistent with a cosmological constant – or, equivalently, with a particular and ubiquitous kind of dark energy – has steadily been accumulating.^[41]

Modern research

General relativity is very successful in providing a framework for accurate models which describe an impressive array of physical phenomena. On the other hand, there are many interesting open questions, and in particular, the theory as a whole is almost certainly incomplete.^[42]

In contrast to all other modern theories of fundamental interactions, general relativity is a classical theory: it does not include the effects of quantum physics. The quest for a quantum version of general relativity addresses one of the most fundamental open questions in physics. While there are promising candidates for such a theory of quantum gravity, notably string theory and loop quantum gravity, there is at present no consistent and complete theory. It has long been hoped that a theory of quantum gravity would also eliminate another problematic feature of general relativity: the presence of spacetime singularities. These singularities are boundaries ("sharp edges") of spacetime at which geometry becomes ill-defined, with the consequence that general relativity itself loses its predictive power. Furthermore, there are so-called singularity theorems which predict that such singularities must exist within the universe if the laws of general relativity were to hold without any quantum modifications. The best-known examples are the singularities associated with the model universes that describe black holes and the beginning of the universe.^[43]

Other attempts to modify general relativity have been made in the context of cosmology. In the modern cosmological models, most energy in the universe is in forms that have never been detected directly, namely dark energy and dark matter. There have been several controversial proposals to obviate the need for these enigmatic forms of matter and energy, by modifying the laws governing gravity and the dynamics of cosmic expansion, for example modified Newtonian dynamics.^[44]

Beyond the challenges of quantum effects and cosmology, research on general relativity is rich with possibilities for further exploration: mathematical relativists explore the nature of singularities and the fundamental properties of Einstein's equations,^[45] ever more comprehensive computer simulations of specific spacetimes (such as those describing merging black holes) are run,^[46] and the race for the first direct detection of gravitational waves continues apace.^[47] More than ninety years after the theory was first published, research is more active than ever.^[48]

Big Bang

From Wikipedia, the free encyclopedia

According to the Big Bang model, the universe expanded from an extremely dense and hot state and continues to expand today.

The Big Bang theory is the prevailing cosmological model for the earliest known periods of the universe.^[1][2][3] It states that the Universe was in a very high density state and then expanded.^[4][5] If the known laws of physics are extrapolated beyond where they are valid there is a singularity. Modern measurements place this moment at approximately 13.8 billion years ago, which is thus considered the age of the universe.^[6] After the initial expansion, the Universe cooled sufficiently to allow the formation of subatomic particles, and later simple atoms. Giant clouds of these primordial elements later coalesced through gravity to form stars and galaxies. The Big Bang theory does not provide any explanation for the initial conditions of the Universe; rather, it describes and explains the general evolution of the Universe going forward from that point on.^[4]

Since Georges Lemaître first noted, in 1927, that an expanding universe might be traced back in time to an originating single point, scientists have built on his idea of cosmic expansion. While the scientific community was once divided between supporters of two different expanding universe theories, the Big Bang and the Steady State theory, accumulated empirical evidence provides strong support for the former.^[7] In 1929, Edwin Hubble discovered indications that all galaxies are drifting apart at high speeds. In 1964, the cosmic microwave background radiation was discovered, which was crucial evidence in favor of the Big Bang model, since that theory predicted the existence of background radiation throughout the Universe before it was discovered. The known physical laws of nature can be used to calculate the characteristics of the Universe in detail back in time to an initial state of extreme density and temperature.^[8][9][10]

Overview

History of the Universe - gravitational waves are hypothesized to arise from cosmic inflation, an expansion just after the Big Bang.^{[11][12][13][14]}

Hubble observed that the distances to faraway galaxies were strongly correlated with their redshifts. This was interpreted to mean that all distant galaxies and clusters are receding away from our vantage point with an apparent velocity proportional to their distance: that is, the farther they are, the faster they move away from us, regardless of direction.^[15] According to the Copernican principle (that the Earth is not the center of the Universe), the only remaining interpretation is that all observable regions of the Universe are receding from all others. Since we know that the distance between galaxies increases today, it must mean that in the past galaxies were closer together. The continuous expansion of the Universe implies that the Universe was denser and hotter in the past.

Large particle accelerators can replicate the conditions that prevailed after the earliest moments of the Universe, resulting in confirmation and refinement of the details of the Big Bang model. However, these accelerators can only probe so far into high energy regimes. Consequently, the state of the Universe in the very earliest instants of the Big Bang expansion is still poorly understood and an area of open investigation.

The first subatomic particles included protons, neutrons, and electrons. Though simple atomic nuclei formed within the first three minutes after the Big Bang, thousands of years passed before the first electrically neutral atoms formed. The majority of atoms produced by the Big Bang were hydrogen, along with helium and traces of lithium. Giant clouds of these primordial elements later coalesced through gravity to form stars and galaxies, and the heavier elements were synthesized either within stars or during supernovae.

The Big Bang theory offers a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background, large scale structure, and Hubble's Law.^[16] The framework for the Big Bang model relies on Albert Einstein's theory of general relativity and on simplifying assumptions such as homogeneity and isotropy of space. The governing equations were formulated by Alexander Friedmann, and similar solutions were worked on by Willem de Sitter. Since then, astrophysicists have incorporated observational and theoretical additions into the Big Bang model, and its parametrization as the Lambda-CDM model serves as the framework for current investigations of theoretical cosmology. The Lambda-CDM model is the standard model of Big Bang cosmology, the simplest model that provides a reasonably good account of various observations about the Universe.

Timeline of the Big Bang

Singularity

Extrapolation of the expansion of the Universe backwards in time using general relativity yields an infinite density and temperature at a finite time in the past.^[17] This singularity signals the breakdown of general relativity. How closely we can extrapolate towards the singularity is debated—certainly no closer than the end of the Planck epoch. This singularity is sometimes called "the Big Bang",^[18] but the term can also refer to the early hot, dense phase itself,^{[19][notes 1]} which can be considered the "birth" of our universe. Based on measurements of the expansion using Type Ia supernovae, measurements of temperature fluctuations in the cosmic microwave background, and measurements of the correlation function of galaxies, the Universe has an estimated age of 13.798 ± 0.037 billion years.^[21] The agreement of these three independent measurements strongly supports the ΛCDM model that describes in detail the contents of the Universe.

Inflation and baryogenesis

The earliest phases of the Big Bang are subject to much speculation. In the most common models the Universe was filled homogeneously and isotropically with an incredibly high energy density and huge temperatures and pressures and was very rapidly expanding and cooling. Approximately 10⁻³⁷ seconds into the expansion, a phase transition caused a cosmic inflation, during which the Universe grew exponentially.^[22] After inflation stopped, the Universe consisted of a quark–gluon plasma, as well as all other elementary particles.^[23] Temperatures were so high that the random motions of particles were at relativistic speeds, and particle–antiparticle pairs of all kinds were being continuously created and destroyed in collisions.^[4] At some point an unknown reaction called baryogenesis violated the conservation of baryon number, leading to a very small excess of quarks and leptons over antiquarks and antileptons—of the order of one part in 30 million. This resulted in the predominance of matter over antimatter in the present universe.^[24]

Cooling

Panoramic view of the entire near-infrared sky reveals the distribution of galaxies beyond the Milky Way. Galaxies are color-coded by redshift.

The universe continued to decrease in density and fall in temperature, hence the typical energy of each particle was decreasing. Symmetry breaking phase transitions put the fundamental forces of physics and the parameters of elementary particles into their present form.^[25] After about 10⁻¹¹ seconds, the picture becomes less speculative, since particle energies drop to values that can be attained in particle physics experiments. At about 10⁻⁶ seconds, quarks and gluons combined to form baryons such as protons and neutrons. The small excess of quarks over antiquarks led to a small excess of baryons over antibaryons. The temperature was now no longer high enough to create new proton–antiproton pairs (similarly for neutrons–antineutrons), so a mass annihilation immediately followed, leaving just one in 10¹⁰ of the original protons and neutrons, and none of their antiparticles. A similar process happened at about 1 second for electrons and positrons. After these annihilations, the remaining protons, neutrons and electrons were no longer moving relativistically and the energy density of the Universe was dominated by photons (with a minor contribution from neutrinos).

A few minutes into the expansion, when the temperature was about a billion (one thousand million; 10⁹; SI prefix giga-) kelvin and the density was about that of air, neutrons combined with protons to form the Universe's deuterium and helium nuclei in a process called Big Bang nucleosynthesis.^[26] Most protons remained uncombined as hydrogen nuclei. As the Universe cooled, the rest mass energy density of matter came to gravitationally dominate that of the photon radiation. After about 379,000 years the electrons and nuclei combined into atoms (mostly hydrogen); hence the radiation decoupled from matter and continued through space largely unimpeded. This relic radiation is known as the cosmic microwave background radiation.^[27] The chemistry of life may have begun shortly after the Big Bang, 13.8 billion years ago, during a habitable epoch when the Universe was only 10–17 million years old.^[28][29][30]

Structure formation

Over a long period of time, the slightly denser regions of the nearly uniformly distributed matter gravitationally attracted nearby matter and thus grew even denser, forming gas clouds, stars, galaxies, and the other astronomical structures observable today.^[4] The details of this process depend on the amount and type of matter in the Universe. The four possible types of matter are known as cold dark matter, warm dark matter, hot dark matter, and baryonic matter. The best measurements available (from WMAP) show that the data is well-fit by a Lambda-CDM model in which dark matter is assumed to be cold (warm dark matter is ruled out by early reionization^[31]), and is estimated to make up about 23% of the matter/energy of the Universe, while baryonic matter makes up about 4.6%.^[32] 

 

In an "extended model" which includes hot dark matter in the form of neutrinos, then if the "physical baryon density" Ω_bh² is estimated at about 0.023 (this is different from the 'baryon density' Ω_b expressed as a fraction of the total matter/energy density, which as noted above is about 0.046), and the corresponding cold dark matter density Ω_ch² is about 0.11, the corresponding neutrino density Ω_vh² is estimated to be less than 0.0062.^[32]

Cosmic acceleration

Abell 2744 galaxy cluster - Hubble Frontier Fields view.^[33]

Independent lines of evidence from Type Ia supernovae and the CMB imply that the Universe today is dominated by a mysterious form of energy known as dark energy, which apparently permeates all of space. The observations suggest 73% of the total energy density of today's universe is in this form. When the Universe was very young, it was likely infused with dark energy, but with less space and everything closer together, gravity predominated, and it was slowly braking the expansion. But eventually, after numerous billion years of expansion, the growing abundance of dark energy caused the expansion of the universe to slowly begin to accelerate. Dark energy in its simplest formulation takes the form of the cosmological constant term in Einstein's field equations of general relativity, but its composition and mechanism are unknown and, more generally, the details of its equation of state and relationship with the Standard Model of particle physics continue to be investigated both observationally and theoretically.^[34]

All of this cosmic evolution after the inflationary epoch can be rigorously described and modelled by the ΛCDM model of cosmology, which uses the independent frameworks of quantum mechanics and Einstein's General Relativity. As noted above, there is no well-supported model describing the action prior to 10⁻¹⁵ seconds or so.^{[clarification needed]} Apparently a new unified theory of quantum gravitation is needed to break this barrier. Understanding this earliest of eras in the history of the Universe is currently one of the greatest unsolved problems in physics.

Underlying assumptions

The Big Bang theory depends on two major assumptions: the universality of physical laws and the cosmological principle. The cosmological principle states that on large scales the Universe is homogeneous and isotropic.

These ideas were initially taken as postulates, but today there are efforts to test each of them. For example, the first assumption has been tested by observations showing that largest possible deviation of the fine structure constant over much of the age of the universe is of order 10⁻⁵.^[35] Also, general relativity has passed stringent tests on the scale of the Solar System and binary stars.^{[notes 2]}

If the large-scale universe appears isotropic as viewed from Earth, the cosmological principle can be derived from the simpler Copernican principle, which states that there is no preferred (or special) observer or vantage point. To this end, the cosmological principle has been confirmed to a level of 10⁻⁵ via observations of the CMB. The Universe has been measured to be homogeneous on the largest scales at the 10% level.^[36]

Expansion of space

General relativity describes spacetime by a metric, which determines the distances that separate nearby points. The points, which can be galaxies, stars, or other objects, themselves are specified using a coordinate chart or "grid" that is laid down over all spacetime. The cosmological principle implies that the metric should be homogeneous and isotropic on large scales, which uniquely singles out the Friedmann–Lemaître–Robertson–Walker metric (FLRW metric). This metric contains a scale factor, which describes how the size of the Universe changes with time. This enables a convenient choice of a coordinate system to be made, called comoving coordinates. In this coordinate system the grid expands along with the Universe, and objects that are moving only due to the expansion of the Universe remain at fixed points on the grid. While their coordinate distance (comoving distance) remains constant, the physical distance between two such comoving points expands proportionally with the scale factor of the Universe.^[37]
The Big Bang is not an explosion of matter moving outward to fill an empty universe. Instead, space itself expands with time everywhere and increases the physical distance between two comoving points. In other words, the Big Bang is not an explosion in space, but rather an expansion of space.^[4] Because the FLRW metric assumes a uniform distribution of mass and energy, it applies to our universe only on large scales—local concentrations of matter such as our galaxy are gravitationally bound and as such do not experience the large-scale expansion of space.^[38]

Horizons

An important feature of the Big Bang spacetime is the presence of horizons. Since the Universe has a finite age, and light travels at a finite speed, there may be events in the past whose light has not had time to reach us. This places a limit or a past horizon on the most distant objects that can be observed. Conversely, because space is expanding, and more distant objects are receding ever more quickly, light emitted by us today may never "catch up" to very distant objects. This defines a future horizon, which limits the events in the future that we will be able to influence. The presence of either type of horizon depends on the details of the FLRW model that describes our universe. Our understanding of the Universe back to very early times suggests that there is a past horizon, though in practice our view is also limited by the opacity of the Universe at early times. So our view cannot extend further backward in time, though the horizon recedes in space. If the expansion of the Universe continues to accelerate, there is a future horizon as well.^[39]

History

Etymology

English astronomer Fred Hoyle is credited with coining the term "Big Bang" during a 1949 BBC radio broadcast. It is popularly reported that Hoyle, who favored an alternative "steady state" cosmological model, intended this to be pejorative, but Hoyle explicitly denied this and said it was just a striking image meant to highlight the difference between the two models.^{[40][41][42]:129}

Development

Hubble eXtreme Deep Field (XDF)

XDF size compared to the size of the moon - several thousand galaxies, each consisting of billions of stars, are in this small view.

XDF (2012) view - each light speck is a galaxy - some of these are as old as 13.2 billion years^[43] - the universe is estimated to contain 200 billion galaxies.

XDF image shows fully mature galaxies in the foreground plane - nearly mature galaxies from 5 to 9 billion years ago - protogalaxies, blazing with young stars, beyond 9 billion years.

The Big Bang theory developed from observations of the structure of the Universe and from theoretical considerations. In 1912 Vesto Slipher measured the first Doppler shift of a "spiral nebula" (spiral nebula is the obsolete term for spiral galaxies), and soon discovered that almost all such nebulae were receding from Earth. He did not grasp the cosmological implications of this fact, and indeed at the time it was highly controversial whether or not these nebulae were "island universes" outside our Milky Way.^[44][45] Ten years later, Alexander Friedmann, a Russian cosmologist and mathematician, derived the Friedmann equations from Albert Einstein's equations of general relativity, showing that the Universe might be expanding in contrast to the static universe model advocated by Einstein at that time.^[46] In 1924 Edwin Hubble's measurement of the great distance to the nearest spiral nebulae showed that these systems were indeed other galaxies. Independently deriving Friedmann's equations in 1927, Georges Lemaître, a Belgian physicist and Roman Catholic priest, proposed that the inferred recession of the nebulae was due to the expansion of the universe.^[47]

In 1931 Lemaître went further and suggested that the evident expansion of the Universe, if projected back in time, meant that the further in the past the smaller the Universe was, until at some finite time in the past all the mass of the Universe was concentrated into a single point, a "primeval atom" where and when the fabric of time and space came into existence.^[48]

Starting in 1924, Hubble painstakingly developed a series of distance indicators, the forerunner of the cosmic distance ladder, using the 100-inch (2,500 mm) Hooker telescope at Mount Wilson Observatory. This allowed him to estimate distances to galaxies whose redshifts had already been measured, mostly by Slipher. In 1929 Hubble discovered a correlation between distance and recession velocity—now known as Hubble's law.^[15][49] Lemaître had already shown that this was expected, given the Cosmological Principle.^[34]

In the 1920s and 1930s almost every major cosmologist preferred an eternal steady state universe, and several complained that the beginning of time implied by the Big Bang imported religious concepts into physics; this objection was later repeated by supporters of the steady state theory.^[50] This perception was enhanced by the fact that the originator of the Big Bang theory, Monsignor Georges Lemaître, was a Roman Catholic priest.^[51] Arthur Eddington agreed with Aristotle that the Universe did not have a beginning in time, viz., that matter is eternal. A beginning in time was "repugnant" to him.^[52][53] Lemaître, however, thought that

If the world has begun with a single quantum, the notions of space and time would altogether fail to have any meaning at the beginning; they would only begin to have a sensible meaning when the original quantum had been divided into a sufficient number of quanta. If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time.^[54]

During the 1930s other ideas were proposed as non-standard cosmologies to explain Hubble's observations, including the Milne model,^[55] the oscillatory universe (originally suggested by Friedmann, but advocated by Albert Einstein and Richard Tolman)^[56] and Fritz Zwicky's tired light hypothesis.^[57]

After World War II, two distinct possibilities emerged. One was Fred Hoyle's steady state model, whereby new matter would be created as the Universe seemed to expand. In this model the Universe is roughly the same at any point in time.^[58] The other was Lemaître's Big Bang theory, advocated and developed by George Gamow, who introduced big bang nucleosynthesis (BBN)^[59] and whose associates, Ralph Alpher and Robert Herman, predicted the cosmic microwave background radiation (CMB).^[60] Ironically, it was Hoyle who coined the phrase that came to be applied to Lemaître's theory, referring to it as "this big bang idea" during a BBC Radio broadcast in March 1949.^{[42]:129[notes 3]} For a while, support was split between these two theories. Eventually, the observational evidence, most notably from radio source counts, began to favor Big Bang over Steady State. The discovery and confirmation of the cosmic microwave background radiation in 1964^[62] secured the Big Bang as the best theory of the origin and evolution of the Universe. Much of the current work in cosmology includes understanding how galaxies form in the context of the Big Bang, understanding the physics of the Universe at earlier and earlier times, and reconciling observations with the basic theory.

Significant progress in Big Bang cosmology have been made since the late 1990s as a result of advances in telescope technology as well as the analysis of data from satellites such as COBE,^[63] the Hubble Space Telescope and WMAP.^[64] Cosmologists now have fairly precise and accurate measurements of many of the parameters of the Big Bang model, and have made the unexpected discovery that the expansion of the Universe appears to be accelerating.

Observational evidence

Artist's depiction of the WMAP satellite gathering data to help scientists understand the Big Bang

"[The] big bang picture is too firmly grounded in data from every area to be proved invalid in its general features."

Lawrence Krauss^[65]

The earliest and most direct observational evidence of the validity of the theory are the expansion of the Universe according to Hubble's law (as indicated by the redshifts of galaxies), discovery and measurement of the cosmic microwave background and the relative abundances of light elements produced by Big Bang nucleosynthesis. More recent evidence includes observations of galaxy formation and evolution, and the distribution of large-scale cosmic structures,^[66] These are sometimes called the "four pillars" of the Big Bang theory.^[67]

Precise modern models of the Big Bang appeal to various exotic physical phenomena that have not been observed in terrestrial laboratory experiments or incorporated into the Standard Model of particle physics. Of these features, dark matter is currently subjected to the most active laboratory investigations.^[68] Remaining issues include the cuspy halo problem and the dwarf galaxy problem of cold dark matter. Dark energy is also an area of intense interest for scientists, but it is not clear whether direct detection of dark energy will be possible.^[69] Inflation and baryogenesis remain more speculative features of current Big Bang models. Viable, quantitative explanations for such phenomena are still being sought. These are currently unsolved problems in physics.

Hubble's law and the expansion of space

Observations of distant galaxies and quasars show that these objects are redshifted—the light emitted from them has been shifted to longer wavelengths. This can be seen by taking a frequency spectrum of an object and matching the spectroscopic pattern of emission lines or absorption lines corresponding to atoms of the chemical elements interacting with the light. These redshifts are uniformly isotropic, distributed evenly among the observed objects in all directions. If the redshift is interpreted as a Doppler shift, the recessional velocity of the object can be calculated. For some galaxies, it is possible to estimate distances via the cosmic distance ladder. When the recessional velocities are plotted against these distances, a linear relationship known as Hubble's law is observed:^[15]

v = H₀D,

where

• v is the recessional velocity of the galaxy or other distant object,
• D is the comoving distance to the object, and
• H₀ is Hubble's constant, measured to be 70.4 +1.3
  −1.4 km/s/Mpc by the WMAP probe.^[32]

Hubble's law has two possible explanations. Either we are at the center of an explosion of galaxies—which is untenable given the Copernican principle—or the Universe is uniformly expanding everywhere. This universal expansion was predicted from general relativity by Alexander Friedmann in 1922^[46] and Georges Lemaître in 1927,^[47] well before Hubble made his 1929 analysis and observations, and it remains the cornerstone of the Big Bang theory as developed by Friedmann, Lemaître, Robertson, and Walker.

The theory requires the relation v = HD to hold at all times, where D is the comoving distance, v is the recessional velocity, and v, H, and D vary as the Universe expands (hence we write H₀ to denote the present-day Hubble "constant"). For distances much smaller than the size of the observable universe, the Hubble redshift can be thought of as the Doppler shift corresponding to the recession velocity v. However, the redshift is not a true Doppler shift, but rather the result of the expansion of the Universe between the time the light was emitted and the time that it was detected.^[70]

That space is undergoing metric expansion is shown by direct observational evidence of the Cosmological principle and the Copernican principle, which together with Hubble's law have no other explanation. Astronomical redshifts are extremely isotropic and homogeneous,^[15] supporting the Cosmological principle that the Universe looks the same in all directions, along with much other evidence. If the redshifts were the result of an explosion from a center distant from us, they would not be so similar in different directions.

Measurements of the effects of the cosmic microwave background radiation on the dynamics of distant astrophysical systems in 2000 proved the Copernican principle, that, on a cosmological scale, the Earth is not in a central position.^[71] Radiation from the Big Bang was demonstrably warmer at earlier times throughout the Universe. Uniform cooling of the cosmic microwave background over billions of years is explainable only if the Universe is experiencing a metric expansion, and excludes the possibility that we are near the unique center of an explosion.

Cosmic microwave background radiation

9 year WMAP image of the cosmic microwave background radiation (2012).^[72][73] The radiation is isotropic to roughly one part in 100,000.^[74]

In 1964 Arno Penzias and Robert Wilson serendipitously discovered the cosmic background radiation, an omnidirectional signal in the microwave band.^[62] Their discovery provided substantial confirmation of the general CMB predictions: the radiation was found to be consistent with an almost perfect black body spectrum in all directions; this spectrum has been redshifted by the expansion of the Universe, and today corresponds to approximately 2.725 K. This tipped the balance of evidence in favor of the Big Bang model, and Penzias and Wilson were awarded a Nobel Prize in 1978.

The cosmic microwave background spectrum measured by the FIRAS instrument on the COBE satellite is the most-precisely measured black body spectrum in nature.^[75] The data points and error bars on this graph are obscured by the theoretical curve.

The surface of last scattering corresponding to emission of the CMB occurs shortly after recombination, the epoch when neutral hydrogen becomes stable. Prior to this, the Universe comprised a hot dense photon-baryon plasma sea where photons were quickly scattered from free charged particles. Peaking at around 372±14 kyr,^[31] the mean free path for a photon becomes long enough to reach the present day and the Universe becomes transparent.

In 1989 NASA launched the Cosmic Background Explorer satellite (COBE). Its findings were consistent with predictions regarding the CMB, finding a residual temperature of 2.726 K (more recent measurements have revised this figure down slightly to 2.725 K) and providing the first evidence for fluctuations (anisotropies) in the CMB, at a level of about one part in 10⁵.^[63] John C. Mather and George Smoot were awarded the Nobel Prize for their leadership in this work. During the following decade, CMB anisotropies were further investigated by a large number of ground-based and balloon experiments. In 2000–2001 several experiments, most notably BOOMERanG, found the shape of the universe to be spatially almost flat by measuring the typical angular size (the size on the sky) of the anisotropies.

In early 2003 the first results of the Wilkinson Microwave Anisotropy Probe (WMAP) were released, yielding what were at the time the most accurate values for some of the cosmological parameters. The results disproved several specific cosmic inflation models, but are consistent with the inflation theory in general.^[64] The Planck space probe was launched in May 2009. Other ground and balloon based cosmic microwave background experiments are ongoing.

Abundance of primordial elements

Using the Big Bang model it is possible to calculate the concentration of helium-4, helium-3, deuterium, and lithium-7 in the Universe as ratios to the amount of ordinary hydrogen.^[26] The relative abundances depend on a single parameter, the ratio of photons to baryons. This value can be calculated independently from the detailed structure of CMB fluctuations. The ratios predicted (by mass, not by number) are about 0.25 for 4He/H, about 10⁻³ for 2H/H, about 10⁻⁴ for 3He/H and about 10⁻⁹ for 7Li/H.^[26]
The measured abundances all agree at least roughly with those predicted from a single value of the baryon-to-photon ratio. The agreement is excellent for deuterium, close but formally discrepant for 4He, and off by a factor of two for 7Li; in the latter two cases there are substantial systematic uncertainties. Nonetheless, the general consistency with abundances predicted by Big Bang nucleosynthesis is strong evidence for the Big Bang, as the theory is the only known explanation for the relative abundances of light elements, and it is virtually impossible to "tune" the Big Bang to produce much more or less than 20–30% helium.^[76] Indeed there is no obvious reason outside of the Big Bang that, for example, the young universe (i.e., before star formation, as determined by studying matter supposedly free of stellar nucleosynthesis products) should have more helium than deuterium or more deuterium than 3He, and in constant ratios, too.

Galactic evolution and distribution

Detailed observations of the morphology and distribution of galaxies and quasars are in agreement with the current state of the Big Bang theory. A combination of observations and theory suggest that the first quasars and galaxies formed about a billion years after the Big Bang, and since then larger structures have been forming, such as galaxy clusters and superclusters. Populations of stars have been aging and evolving, so that distant galaxies (which are observed as they were in the early universe) appear very different from nearby galaxies (observed in a more recent state). Moreover, galaxies that formed relatively recently appear markedly different from galaxies formed at similar distances but shortly after the Big Bang. These observations are strong arguments against the steady-state model. Observations of star formation, galaxy and quasar distributions and larger structures agree well with Big Bang simulations of the formation of structure in the Universe and are helping to complete details of the theory.^[77][78]

Primordial gas clouds

Focal plane of BICEP2 telescope under a microscope - may have detected gravitational waves from the infant universe.^{[11][12][13][14]}

In 2011 astronomers found what they believe to be pristine clouds of primordial gas, by analyzing absorption lines in the spectra of distant quasars. Before this discovery, all other astronomical objects have been observed to contain heavy elements that are formed in stars. These two clouds of gas contain no elements heavier than hydrogen and deuterium.^[79][80] Since the clouds of gas have no heavy elements, they likely formed in the first few minutes after the Big Bang, during Big Bang nucleosynthesis. Their composition matches the composition predicted from Big Bang nucleosynthesis. This provides direct evidence that there was a period in the history of the Universe before the formation of the first stars, when most ordinary matter existed in the form of clouds of neutral hydrogen.^{[citation needed]}

Other lines of evidence

The age of universe as estimated from the Hubble expansion and the CMB is now in good agreement with other estimates using the ages of the oldest stars, both as measured by applying the theory of stellar evolution to globular clusters and through radiometric dating of individual Population II stars.^[81]

The prediction that the CMB temperature was higher in the past has been experimentally supported by observations of very low temperature absorption lines in gas clouds at high redshift.^[82] This prediction also implies that the amplitude of the Sunyaev–Zel'dovich effect in clusters of galaxies does not depend directly on redshift. Observations have found this to be roughly true, but this effect depends on cluster properties that do change with cosmic time, making precise measurements difficult.^[83][84]

On 17 March 2014, astronomers at the Harvard-Smithsonian Center for Astrophysics announced the apparent detection of primordial gravitational waves, which, if confirmed, may provide strong evidence for inflation and the Big Bang.^{[11][12][13][14]} However, on 19 June 2014, lowered confidence in confirming the findings was reported;^[85][86][87] and on 19 September 2014, even more lowered confidence.^[88][89]

Related issues in physics

Baryon asymmetry

It is not yet understood why the Universe has more matter than antimatter.^[90] It is generally assumed that when the Universe was young and very hot, it was in statistical equilibrium and contained equal numbers of baryons and antibaryons. However, observations suggest that the Universe, including its most distant parts, is made almost entirely of matter. A process called baryogenesis was hypothesized to account for the asymmetry. For baryogenesis to occur, the Sakharov conditions must be satisfied. These require that baryon number is not conserved, that C-symmetry and CP-symmetry are violated and that the Universe depart from thermodynamic equilibrium.^[91] All these conditions occur in the Standard Model, but the effect is not strong enough to explain the present baryon asymmetry.

Dark energy

The accelerated expansion of space. In this illustration, time flows from bottom to top.

Measurements of the redshift–magnitude relation for type Ia supernovae indicate that the expansion of the Universe has been accelerating since the Universe was about half its present age. To explain this acceleration, general relativity requires that much of the energy in the Universe consists of a component with large negative pressure, dubbed "dark energy". Dark energy, though speculative, solves numerous problems. Measurements of the cosmic microwave background indicate that the Universe is very nearly spatially flat, and therefore according to general relativity the Universe must have almost exactly the critical density of mass/energy. But the mass density of the Universe can be measured from its gravitational clustering, and is found to have only about 30% of the critical density.^[34] Since theory suggests that dark energy does not cluster in the usual way it is the best explanation for the "missing" energy density. Dark energy also helps to explain two geometrical measures of the overall curvature of the Universe, one using the frequency of gravitational lenses, and the other using the characteristic pattern of the large-scale structure as a cosmic ruler.

Negative pressure is believed to be a property of vacuum energy, but the exact nature and existence of dark energy remains one of the great mysteries of the Big Bang. Possible candidates include a cosmological constant and quintessence. Results from the WMAP team in 2008 are in accordance with a universe that consists of 73% dark energy, 23% dark matter, 4.6% regular matter and less than 1% neutrinos.^[32] According to theory, the energy density in matter decreases with the expansion of the Universe, but the dark energy density remains constant (or nearly so) as the Universe expands. Therefore matter made up a larger fraction of the total energy of the Universe in the past than it does today, but its fractional contribution will fall in the far future as dark energy becomes even more dominant.

Dark matter

Chart shows the proportion of different components of the universe  – about 95% is dark matter and dark energy.

During the 1970s and 80s, various observations showed that there is not sufficient visible matter in the Universe to account for the apparent strength of gravitational forces within and between galaxies. This led to the idea that up to 90% of the matter in the Universe is dark matter that does not emit light or interact with normal baryonic matter. In addition, the assumption that the Universe is mostly normal matter led to predictions that were strongly inconsistent with observations. In particular, the Universe today is far more lumpy and contains far less deuterium than can be accounted for without dark matter. While dark matter has always been controversial, it is inferred by various observations: the anisotropies in the CMB, galaxy cluster velocity dispersions, large-scale structure distributions, gravitational lensing studies, and X-ray measurements of galaxy clusters.^[92]

Indirect evidence for dark matter comes from its gravitational influence on other matter, as no dark matter particles have been observed in laboratories. Many particle physics candidates for dark matter have been proposed, and several projects to detect them directly are underway.^[93]

Globular cluster age

In the mid-1990s observations of globular clusters appeared to be inconsistent with the Big Bang theory. Computer simulations that matched the observations of the stellar populations of globular clusters suggested that they were about 15 billion years old, which conflicted with the 13.8 billion year age of the Universe. This issue was partially resolved in the late 1990s when new computer simulations, which included the effects of mass loss due to stellar winds, indicated a much younger age for globular clusters.^[94] There remain some questions as to how accurately the ages of the clusters are measured, but it is clear that observations of globular clusters no longer appear inconsistent with the Big Bang theory.

Problems

There are generally considered to be three outstanding problems with the Big Bang theory: the horizon problem, the flatness problem, and the magnetic monopole problem. The most common answer to these problems is inflationary theory; however, since this creates new problems, other options have been proposed, such as the Weyl curvature hypothesis.^[95][96]

Horizon problem

The horizon problem results from the premise that information cannot travel faster than light. In a universe of finite age this sets a limit—the particle horizon—on the separation of any two regions of space that are in causal contact.^[97] The observed isotropy of the CMB is problematic in this regard: if the Universe had been dominated by radiation or matter at all times up to the epoch of last scattering, the particle horizon at that time would correspond to about 2 degrees on the sky. There would then be no mechanism to cause wider regions to have the same temperature.
A resolution to this apparent inconsistency is offered by inflationary theory in which a homogeneous and isotropic scalar energy field dominates the Universe at some very early period (before baryogenesis). During inflation, the Universe undergoes exponential expansion, and the particle horizon expands much more rapidly than previously assumed, so that regions presently on opposite sides of the observable universe are well inside each other's particle horizon. The observed isotropy of the CMB then follows from the fact that this larger region was in causal contact before the beginning of inflation.

Heisenberg's uncertainty principle predicts that during the inflationary phase there would be quantum thermal fluctuations, which would be magnified to cosmic scale. These fluctuations serve as the seeds of all current structure in the Universe. Inflation predicts that the primordial fluctuations are nearly scale invariant and Gaussian, which has been accurately confirmed by measurements of the CMB.

If inflation occurred, exponential expansion would push large regions of space well beyond our observable horizon.

Flatness problem

The overall geometry of the universe is determined by whether the Omega cosmological parameter is less than, equal to or greater than 1. Shown from top to bottom are a closed universe with positive curvature, a hyperbolic universe with negative curvature and a flat universe with zero curvature.

The flatness problem (also known as the oldness problem) is an observational problem associated with a Friedmann–Lemaître–Robertson–Walker metric.^[97] The Universe may have positive, negative, or zero spatial curvature depending on its total energy density. Curvature is negative if its density is less than the critical density, positive if greater, and zero at the critical density, in which case space is said to be flat. The problem is that any small departure from the critical density grows with time, and yet the Universe today remains very close to flat.^{[notes 4]} Given that a natural timescale for departure from flatness might be the Planck time, 10⁻⁴³ seconds,^[4] the fact that the Universe has reached neither a heat death nor a Big Crunch after billions of years requires an explanation. For instance, even at the relatively late age of a few minutes (the time of nucleosynthesis), the Universe density must have been within one part in 10¹⁴ of its critical value, or it would not exist as it does today.^[98]

A resolution to this problem is offered by inflationary theory. During the inflationary period, spacetime expanded to such an extent that its curvature would have been smoothed out. Thus, it is theorized that inflation drove the Universe to a very nearly spatially flat state, with almost exactly the critical density.^{[citation needed]}

Magnetic monopoles

The magnetic monopole objection was raised in the late 1970s. Grand unification theories predicted topological defects in space that would manifest as magnetic monopoles. These objects would be produced efficiently in the hot early universe, resulting in a density much higher than is consistent with observations, given that no monopoles have been found. This problem is also resolved by cosmic inflation, which removes all point defects from the observable universe, in the same way that it drives the geometry to flatness.^[97]

The future according to the Big Bang theory

Before observations of dark energy, cosmologists considered two scenarios for the future of the Universe. If the mass density of the Universe were greater than the critical density, then the Universe would reach a maximum size and then begin to collapse. It would become denser and hotter again, ending with a state similar to that in which it started—a Big Crunch.^[39] Alternatively, if the density in the Universe were equal to or below the critical density, the expansion would slow down but never stop. Star formation would cease with the consumption of interstellar gas in each galaxy; stars would burn out leaving white dwarfs, neutron stars, and black holes. Very gradually, collisions between these would result in mass accumulating into larger and larger black holes. The average temperature of the Universe would asymptotically approach absolute zero—a Big Freeze. Moreover, if the proton were unstable, then baryonic matter would disappear, leaving only radiation and black holes. 

Eventually, black holes would evaporate by emitting Hawking radiation. The entropy of the Universe would increase to the point where no organized form of energy could be extracted from it, a scenario known as heat death.
Modern observations of accelerating expansion imply that more and more of the currently visible universe will pass beyond our event horizon and out of contact with us. The eventual result is not known. The ΛCDM model of the Universe contains dark energy in the form of a cosmological constant. This theory suggests that only gravitationally bound systems, such as galaxies, will remain together, and they too will be subject to heat death as the Universe expands and cools. Other explanations of dark energy, called phantom energy theories, suggest that ultimately galaxy clusters, stars, planets, atoms, nuclei, and matter itself will be torn apart by the ever-increasing expansion in a so-called Big Rip.^[99]

Speculative physics beyond the Big Bang theory

This is an artist's concept of the metric expansion of space, where space (including hypothetical non-observable portions of the universe) is represented at each time by the circular sections. Note on the left the dramatic expansion (not to scale) occurring in the inflationary epoch, and at the center the expansion acceleration. The scheme is decorated with WMAP images on the left and with the representation of stars at the appropriate level of development.

While the Big Bang model is well established in cosmology, it is likely to be refined. The equations of classical general relativity indicate a singularity at the origin of cosmic time, although this conclusion depends on several assumptions and the equations break down at any time before the Universe reached the Planck temperature. A correct treatment of quantum gravity may avoid the would-be singularity.^[100]

It is not known what could have caused the singularity to come into existence (if it had a cause), or how and why it originated, though speculation abounds in the field of cosmogony. Some proposals, each of which entails untested hypotheses, are:

• Models including the Hartle–Hawking no-boundary condition, in which the whole of space-time is finite; the Big Bang does represent the limit of time but without the need for a singularity.^[101]
• Big Bang lattice model, states that the Universe at the moment of the Big Bang consists of an infinite lattice of fermions, which is smeared over the fundamental domain so it has rotational, translational and gauge symmetry. The symmetry is the largest symmetry possible and hence the lowest entropy of any state.^[102]
• Brane cosmology models, in which inflation is due to the movement of branes in string theory; the pre-Big Bang model; the ekpyrotic model, in which the Big Bang is the result of a collision between branes and the cyclic model, a variant of the ekpyrotic model in which collisions occur periodically. In the latter model the Big Bang was preceded by a Big Crunch and the Universe cycles from one process to the other.^{[103][104][105][106]}
• Eternal inflation, in which universal inflation ends locally here and there in a random fashion, each end-point leading to a bubble universe, expanding from its own big bang.^[107][108]

Proposals in the last two categories, see the Big Bang as an event in either a much larger and older universe or in a multiverse.

Religious and philosophical interpretations

As a description of the origin of the Universe, the Big Bang has significant bearing on religion and philosophy.^[109][110] As a result, it has become one of the liveliest areas in the discourse between science and religion.^[111] Some believe the Big Bang implies a creator,^[112] and some see its mention in their holy books,^[113] while others argue that Big Bang cosmology makes the notion of a creator superfluous.^[110][114]