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192-418: It is referred to as the standard model of Big Bang cosmology because it is the simplest model that provides a reasonably good account of: The model assumes that general relativity is the correct theory of gravity on cosmological scales. It emerged in the late 1990s as a concordance cosmology , after a period of time when disparate observed properties of the universe appeared mutually inconsistent, and there

384-472: A {\displaystyle a} , e.g. a − 3 {\displaystyle a^{-3}} for matter etc., the Friedmann equation can be conveniently rewritten in terms of the various density parameters as where w {\displaystyle w} is the equation of state parameter of dark energy, and assuming negligible neutrino mass (significant neutrino mass requires

576-441: A Belgian physicist and Roman Catholic priest , proposed that the recession of the nebulae was due to the expansion of the universe. He inferred the relation that Hubble would later observe, given the cosmological principle. 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

768-582: A Russian cosmologist and mathematician , derived the Friedmann equations from the Einstein field equations, showing that the universe might be expanding in contrast to the static universe model advocated by Albert Einstein at that time. In 1924, American astronomer Edwin Hubble 's measurement of the great distance to the nearest spiral nebulae showed that these systems were indeed other galaxies. Starting that same year, Hubble painstakingly developed

960-484: 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 Friedmann–Lemaître–Robertson–Walker (FLRW) metric that describes the expansion of the 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

1152-543: A pair of black holes merging . The simplest type of such a wave can be visualized by its action on a ring of freely floating particles. A sine wave propagating through such a ring towards the reader distorts the ring in a characteristic, rhythmic fashion (animated image to the right). Since Einstein's equations are non-linear , arbitrarily strong gravitational waves do not obey linear superposition , making their description difficult. However, linear approximations of gravitational waves are sufficiently accurate to describe

1344-570: A body in accordance with Newton's second law of motion , which states that the net force acting on a body is equal to that body's (inertial) mass multiplied by its acceleration . The preferred inertial motions are related to the geometry of space and time: in the standard reference frames of classical mechanics, objects in free motion move along straight lines at constant speed. In modern parlance, their paths are geodesics , straight world lines in curved spacetime . Conversely, one might expect that inertial motions, once identified by observing

1536-434: A comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements , the cosmic microwave background (CMB) radiation , and large-scale structure . The uniformity of the universe, known as the flatness problem , is explained through cosmic inflation : a sudden and very rapid expansion of space during the earliest moments. Extrapolating this cosmic expansion backward in time using

1728-560: A computer, or by considering small perturbations of exact solutions. In the field of numerical relativity , powerful computers are employed to simulate the geometry of spacetime and to solve Einstein's equations for interesting situations such as two colliding black holes. In principle, such methods may be applied to any system, given sufficient computer resources, and may address fundamental questions such as naked singularities . Approximate solutions may also be found by perturbation theories such as linearized gravity and its generalization,

1920-508: A curiosity among physical theories. It was clearly superior to Newtonian gravity , being consistent with special relativity and accounting for several effects unexplained by the Newtonian theory. Einstein showed in 1915 how his theory explained the anomalous perihelion advance of the planet Mercury without any arbitrary parameters (" fudge factors "), and in 1919 an expedition led by Eddington confirmed general relativity's prediction for

2112-530: A curved generalization of Minkowski space. The metric tensor that defines the geometry—in particular, how lengths and angles are measured—is not the Minkowski metric of special relativity, it is a generalization known as a semi- or pseudo-Riemannian metric. Furthermore, each Riemannian metric is naturally associated with one particular kind of connection, the Levi-Civita connection , and this is, in fact,

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2304-539: A curved geometry of spacetime in general relativity; there is no gravitational force deflecting objects from their natural, straight paths. Instead, gravity corresponds to changes in the properties of space and time, which in turn changes the straightest-possible paths that objects will naturally follow. The curvature is, in turn, caused by the energy–momentum of matter. Paraphrasing the relativist John Archibald Wheeler , spacetime tells matter how to move; matter tells spacetime how to curve. While general relativity replaces

2496-597: A gravitational field (cf. below ). The actual measurements show that free-falling frames are the ones in which light propagates as it does in special relativity. The generalization of this statement, namely that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames, is known as the Einstein equivalence principle , a crucial guiding principle for generalizing special-relativistic physics to include gravity. The same experimental data shows that time as measured by clocks in

2688-471: A gravitational field— proper time , to give the technical term—does not follow the rules of special relativity. In the language of spacetime geometry, it is not measured by the Minkowski metric . As in the Newtonian case, this is suggestive of a more general geometry. At small scales, all reference frames that are in free fall are equivalent, and approximately Minkowskian. Consequently, we are now dealing with

2880-425: A laboratory, and its value is extremely small compared to vacuum energy theoretical predictions . The ΛCDM model has been shown to satisfy the cosmological principle , which states that, on a large-enough scale, the universe looks the same in all directions ( isotropy ) and from every location ( homogeneity ); "the universe looks the same whoever and wherever you are." The cosmological principle exists because when

3072-450: A massive central body M is given by A conservative total force can then be obtained as its negative gradient where L is the angular momentum . The first term represents the force of Newtonian gravity , which is described by the inverse-square law. The second term represents the centrifugal force in the circular motion. The third term represents the relativistic effect. There are alternatives to general relativity built upon

3264-516: A modification of the Einstein field equations and the Friedmann equations as seen in proposals such as modified gravity theory (MOG theory) or tensor–vector–scalar gravity theory (TeVeS theory). Other proposals by theoretical astrophysicists of cosmological alternatives to Einstein's general relativity that attempt to account for dark energy or dark matter include f(R) gravity , scalar–tensor theories such as galileon  [ ko ] theories (see Galilean invariance ), brane cosmologies ,

3456-399: A more complex equation). The various Ω {\displaystyle \Omega } parameters add up to 1 {\displaystyle 1} by construction. In the general case this is integrated by computer to give the expansion history a ( t ) {\displaystyle a(t)} and also observable distance–redshift relations for any chosen values of

3648-550: A more generic early hot, dense phase of the universe. In either case, "the Big Bang" as an event is also colloquially referred to as the "birth" of our universe since it represents the point in history where the universe can be verified to have entered into a regime where the laws of physics as we understand them (specifically general relativity and the Standard Model of particle physics ) work. Based on measurements of

3840-702: A number of exact solutions are known, although only a few have direct physical applications. The best-known exact solutions, and also those most interesting from a physics point of view, are the Schwarzschild solution , the Reissner–Nordström solution and the Kerr metric , each corresponding to a certain type of black hole in an otherwise empty universe, and the Friedmann–Lemaître–Robertson–Walker and de Sitter universes , each describing an expanding cosmos. Exact solutions of great theoretical interest include

4032-453: A problem, however, as there is a lack of a self-consistent theory of quantum gravity . It is not yet known how gravity can be unified with the three non-gravitational forces: strong , weak and electromagnetic . Einstein's theory has astrophysical implications, including the prediction of black holes —regions of space in which space and time are distorted in such a way that nothing, not even light , can escape from them. Black holes are

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4224-504: A process in the very early universe has reached thermal equilibrium is the ratio between the rate of the process (usually rate of collisions between particles) and the Hubble parameter . The larger the ratio, the more time particles had to thermalize before they were too far away from each other. According to the Big Bang models, the universe at the beginning was very hot and very compact, and since then it has been expanding and cooling. In

4416-471: A rate that accelerates proportionally with distance. Independent of Friedmann's work, and independent of Hubble's observations, physicist Georges Lemaître proposed that the universe emerged from a "primeval atom " in 1931, introducing the modern notion of the Big Bang. Various cosmological models of the Big Bang explain the evolution of the observable universe from the earliest known periods through its subsequent large-scale form. These models offer

4608-659: A relativistic theory of gravity. After numerous detours and false starts, his work culminated in the presentation to the Prussian Academy of Science in November 1915 of what are now known as the Einstein field equations, which form the core of Einstein's general theory of relativity. These equations specify how the geometry of space and time is influenced by whatever matter and radiation are present. A version of non-Euclidean geometry , called Riemannian geometry , enabled Einstein to develop general relativity by providing

4800-467: A series of distance indicators, the forerunner of the cosmic distance ladder , using the 100-inch (2.5 m) 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 recessional velocity —now known as Hubble's law. Independently deriving Friedmann's equations in 1927, Georges Lemaître ,

4992-452: A surrounding space, the Big Bang only describes the intrinsic expansion of the contents of the universe. Another issue pointed out by Santhosh Mathew is that bang implies sound, which is not an important feature of the model. An attempt to find a more suitable alternative was not successful. The Big Bang models developed from observations of the structure of the universe and from theoretical considerations. In 1912, Vesto Slipher measured

5184-430: A temperature of approximately 10 degrees Celsius. Even the very concept of a particle breaks down in these conditions. A proper understanding of this period awaits the development of a theory of quantum gravity . The Planck epoch was succeeded by the grand unification epoch beginning at 10 seconds, where gravitation separated from the other forces as the universe's temperature fell. At approximately 10 seconds into

5376-490: A university matriculation examination, and, despite the shortness of the book, a fair amount of patience and force of will on the part of the reader. The author has spared himself no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the whole, in the sequence and connection in which they actually originated." General relativity can be understood by examining its similarities with and departures from classical physics. The first step

5568-539: A wave train traveling through empty space or Gowdy universes , varieties of an expanding cosmos filled with gravitational waves. But for gravitational waves produced in astrophysically relevant situations, such as the merger of two black holes, numerical methods are presently the only way to construct appropriate models. General relativity differs from classical mechanics in a number of predictions concerning orbiting bodies. It predicts an overall rotation ( precession ) of planetary orbits, as well as orbital decay caused by

5760-526: Is Minkowskian , and the laws of physics exhibit local Lorentz invariance . The core concept of general-relativistic model-building is that of a solution of Einstein's equations . Given both Einstein's equations and suitable equations for the properties of matter, such a solution consists of a specific semi- Riemannian manifold (usually defined by giving the metric in specific coordinates), and specific matter fields defined on that manifold. Matter and geometry must satisfy Einstein's equations, so in particular,

5952-423: Is a scalar parameter of motion (e.g. the proper time ), and Γ μ α β {\displaystyle \Gamma ^{\mu }{}_{\alpha \beta }} are Christoffel symbols (sometimes called the affine connection coefficients or Levi-Civita connection coefficients) which is symmetric in the two lower indices. Greek indices may take the values: 0, 1, 2, 3 and

Lambda-CDM model - Misplaced Pages Continue

6144-445: Is a universality of free fall (also known as the weak equivalence principle , or the universal equality of inertial and passive-gravitational mass): the trajectory of a test body in free fall depends only on its position and initial speed, but not on any of its material properties. A simplified version of this is embodied in Einstein's elevator experiment , illustrated in the figure on the right: for an observer in an enclosed room, it

6336-505: Is above or below the so-called critical density. During the 1970s, most attention focused on pure-baryonic models, but there were serious challenges explaining the formation of galaxies, given the small anisotropies in the CMB (upper limits at that time). In the early 1980s, it was realized that this could be resolved if cold dark matter dominated over the baryons, and the theory of cosmic inflation motivated models with critical density. During

6528-495: Is accelerating , an observation attributed to an unexplained phenomenon known as dark energy . The Big Bang models offer a comprehensive explanation for a broad range of observed phenomena, including the abundances of the light elements , the CMB , large-scale structure , and Hubble's law . The models depend on two major assumptions: the universality of physical laws and the cosmological principle . The universality of physical laws

6720-422: Is assumed to be cold. (Warm dark matter is ruled out by early reionization .) This CDM is estimated to make up about 23% of the matter/energy of the universe, while baryonic matter makes up about 4.6%. In an "extended model" which includes hot dark matter in the form of neutrinos, then the "physical baryon density" Ω b h 2 {\displaystyle \Omega _{\text{b}}h^{2}}

6912-402: Is based on the propagation of light, and thus on electromagnetism, which could have a different set of preferred frames . But using different assumptions about the special-relativistic frames (such as their being earth-fixed, or in free fall), one can derive different predictions for the gravitational redshift, that is, the way in which the frequency of light shifts as the light propagates through

7104-412: Is called the S 8 {\displaystyle S_{8}} tension. The name "tension" reflects that the disagreement is not merely between two data sets: the many sets of early- and late-time measurements agree well within their own categories, but there is an unexplained difference between values obtained from different points in the evolution of the universe. Such a tension indicates that

7296-582: Is considered the age of the universe . There remain aspects of the observed universe that are not yet adequately explained by the Big Bang models. After its initial expansion, the universe cooled sufficiently to allow the formation of subatomic particles , and later atoms . The unequal abundances of matter and antimatter that allowed this to occur is an unexplained effect known as baryon asymmetry . These primordial elements—mostly hydrogen , with some helium and lithium —later coalesced through gravity , forming early stars and galaxies. Astronomers observe

7488-499: Is curved. The resulting Newton–Cartan theory is a geometric formulation of Newtonian gravity using only covariant concepts, i.e. a description which is valid in any desired coordinate system. In this geometric description, tidal effects —the relative acceleration of bodies in free fall—are related to the derivative of the connection, showing how the modified geometry is caused by the presence of mass. As intriguing as geometric Newtonian gravity may be, its basis, classical mechanics,

7680-405: Is defined in the absence of gravity. For practical applications, it is a suitable model whenever gravity can be neglected. Bringing gravity into play, and assuming the universality of free fall motion, an analogous reasoning as in the previous section applies: there are no global inertial frames . Instead there are approximate inertial frames moving alongside freely falling particles. Translated into

7872-403: Is estimated at 0.023. (This is different from the 'baryon density' Ω b {\displaystyle \Omega _{\text{b}}} expressed as a fraction of the total matter/energy density, which is about 0.046.) The corresponding cold dark matter density Ω c h 2 {\displaystyle \Omega _{\text{c}}h^{2}} is about 0.11, and

Lambda-CDM model - Misplaced Pages Continue

8064-417: Is fairly accurate for a > 0.01 {\displaystyle a>0.01} or t > 10 {\displaystyle t>10} million years. Solving for a ( t ) = 1 {\displaystyle a(t)=1} gives the present age of the universe t 0 {\displaystyle t_{0}} in terms of the other parameters. It follows that

8256-445: Is impossible to decide, by mapping the trajectory of bodies such as a dropped ball, whether the room is stationary in a gravitational field and the ball accelerating, or in free space aboard a rocket that is accelerating at a rate equal to that of the gravitational field versus the ball which upon release has nil acceleration. Given the universality of free fall, there is no observable distinction between inertial motion and motion under

8448-425: 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: v = H 0 D {\displaystyle v=H_{0}D} where Hubble's law implies that

8640-560: Is known as gravitational time dilation. Gravitational redshift has been measured in the laboratory and using astronomical observations. Gravitational time dilation in the Earth's gravitational field has been measured numerous times using atomic clocks , while ongoing validation is provided as a side effect of the operation of the Global Positioning System (GPS). Tests in stronger gravitational fields are provided by

8832-404: Is mass. In special relativity, mass turns out to be part of a more general quantity called the energy–momentum tensor , which includes both energy and momentum densities as well as stress : pressure and shear. Using the equivalence principle, this tensor is readily generalized to curved spacetime. Drawing further upon the analogy with geometric Newtonian gravity, it is natural to assume that

9024-456: Is merely a limiting case of (special) relativistic mechanics. In the language of symmetry : where gravity can be neglected, physics is Lorentz invariant as in special relativity rather than Galilei invariant as in classical mechanics. (The defining symmetry of special relativity is the Poincaré group , which includes translations, rotations, boosts and reflections.) The differences between

9216-493: Is modeled by a cosmological constant term in Einstein field equations of general relativity, but its composition and mechanism are unknown. More generally, the details of its equation of state and relationship with the Standard Model of particle physics continue to be investigated both through observation and theory. All of this cosmic evolution after the inflationary epoch can be rigorously described and modeled by

9408-427: Is no preferred (or special) observer or vantage point. To this end, the cosmological principle has been confirmed to a level of 10 via observations of the temperature of the CMB. At the scale of the CMB horizon, the universe has been measured to be homogeneous with an upper bound on the order of 10% inhomogeneity, as of 1995. An important feature of the Big Bang spacetime is the presence of particle horizons . Since

9600-430: Is now associated with electrically charged black holes . In 1917, Einstein applied his theory to the universe as a whole, initiating the field of relativistic cosmology. In line with contemporary thinking, he assumed a static universe, adding a new parameter to his original field equations—the cosmological constant —to match that observational presumption. By 1929, however, the work of Hubble and others had shown that

9792-457: Is one of b {\displaystyle \mathrm {b} } for baryons , c {\displaystyle \mathrm {c} } for cold dark matter , r a d {\displaystyle \mathrm {rad} } for radiation ( photons plus relativistic neutrinos ), and Λ {\displaystyle \Lambda } for dark energy . Since the densities of various species scale as different powers of

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9984-410: Is one of the underlying principles of the theory of relativity . The cosmological principle states that on large scales the universe is homogeneous and isotropic —appearing the same in all directions regardless of location. These ideas were initially taken as postulates, but later efforts were made to test each of them. For example, the first assumption has been tested by observations showing that

10176-495: Is the Shapiro Time Delay, the phenomenon that light signals take longer to move through a gravitational field than they would in the absence of that field. There have been numerous successful tests of this prediction. In the parameterized post-Newtonian formalism (PPN), measurements of both the deflection of light and the gravitational time delay determine a parameter called γ, which encodes the influence of gravity on

10368-400: Is the only cosmological model consistent with the observed continuing expansion of space, the observed distribution of lighter elements in the universe (hydrogen, helium, and lithium), and the spatial texture of minute irregularities ( anisotropies ) in the CMB radiation. Cosmic inflation also addresses the " horizon problem " in the CMB; indeed, it seems likely that the universe is larger than

10560-409: Is the parametrized post-Newtonian (PPN) formalism, which allows quantitative comparisons between the predictions of general relativity and alternative theories. General relativity has a number of physical consequences. Some follow directly from the theory's axioms, whereas others have become clear only in the course of many years of research that followed Einstein's initial publication. Assuming that

10752-432: Is the proper distance, v {\displaystyle v} is the recessional velocity, and v {\displaystyle v} , H {\displaystyle H} , and D {\displaystyle D} vary as the universe expands (hence we write H 0 {\displaystyle H_{0}} to denote the present-day Hubble "constant"). For distances much smaller than

10944-471: Is the realization that classical mechanics and Newton's law of gravity admit a geometric description. The combination of this description with the laws of special relativity results in a heuristic derivation of general relativity. At the base of classical mechanics is the notion that a body 's motion can be described as a combination of free (or inertial ) motion, and deviations from this free motion. Such deviations are caused by external forces acting on

11136-423: Is the speed of light and G {\displaystyle G} is the gravitational constant . A critical density ρ c r i t {\displaystyle \rho _{\mathrm {crit} }} is the present-day density, which gives zero curvature k {\displaystyle k} , assuming the cosmological constant Λ {\displaystyle \Lambda }

11328-416: Is the time-derivative of the scale factor. The first Friedmann equation gives the expansion rate in terms of the matter+radiation density ρ {\displaystyle \rho } , the curvature k {\displaystyle k} , and the cosmological constant Λ {\displaystyle \Lambda } , where, as usual c {\displaystyle c}

11520-544: Is violated on large scales. Data from the Planck Mission shows hemispheric bias in the cosmic microwave background in two respects: one with respect to average temperature (i.e. temperature fluctuations), the second with respect to larger variations in the degree of perturbations (i.e. densities). The European Space Agency (the governing body of the Planck Mission) has concluded that these anisotropies in

11712-456: Is well documented, both as the redshift of prominent spectral absorption or emission lines in the light from distant galaxies, and as the time dilation in the light decay of supernova luminosity curves. Both effects are attributed to a Doppler shift in electromagnetic radiation as it travels across expanding space. Although this expansion increases the distance between objects that are not under shared gravitational influence, it does not increase

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11904-458: Is zero, regardless of its actual value. Substituting these conditions to the Friedmann equation gives where h ≡ H 0 / ( 100 k m ⋅ s − 1 ⋅ M p c − 1 ) {\displaystyle h\equiv H_{0}/(100\;\mathrm {km{\cdot }s^{-1}{\cdot }Mpc^{-1}} )} is

12096-517: The Planck spacecraft . The discovery of the cosmic microwave background (CMB) in 1964 confirmed a key prediction of the Big Bang cosmology. From that point on, it was generally accepted that the universe started in a hot, dense state and has been expanding over time. The rate of expansion depends on the types of matter and energy present in the universe, and in particular, whether the total density

12288-602: The curvature of spacetime is directly related to the energy and momentum of whatever present matter and radiation . The relation is specified by the Einstein field equations , a system of second-order partial differential equations . Newton's law of universal gravitation , which describes classical gravity, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity, however, are beyond Newton's law of universal gravitation in classical physics . These predictions concern

12480-473: The DGP model , and massive gravity and its extensions such as bimetric gravity . In addition to explaining many pre-2000 observations, the model has made a number of successful predictions: notably the existence of the baryon acoustic oscillation feature, discovered in 2005 in the predicted location; and the statistics of weak gravitational lensing , first observed in 2000 by several teams. The polarization of

12672-432: The Einstein notation , meaning that repeated indices are summed (i.e. from zero to three). The Christoffel symbols are functions of the four spacetime coordinates, and so are independent of the velocity or acceleration or other characteristics of a test particle whose motion is described by the geodesic equation. In general relativity, the effective gravitational potential energy of an object of mass m revolving around

12864-609: The Gödel universe (which opens up the intriguing possibility of time travel in curved spacetimes), the Taub–NUT solution (a model universe that is homogeneous , but anisotropic ), and anti-de Sitter space (which has recently come to prominence in the context of what is called the Maldacena conjecture ). Given the difficulty of finding exact solutions, Einstein's field equations are also solved frequently by numerical integration on

13056-533: The Hubble Space Telescope and WMAP. 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. "[The] big bang picture is too firmly grounded in data from every area to be proved invalid in its general features." — Lawrence Krauss The earliest and most direct observational evidence of

13248-703: The Hubble diagram of Type Ia supernovae and quasars . This contradicts the cosmological principle. The CMB dipole is hinted at through a number of other observations. First, even within the cosmic microwave background, there are curious directional alignments and an anomalous parity asymmetry that may have an origin in the CMB dipole. Separately, the CMB dipole direction has emerged as a preferred direction in studies of alignments in quasar polarizations, scaling relations in galaxy clusters, strong lensing time delay, Type Ia supernovae, and quasars and gamma-ray bursts as standard candles . The fact that all these independent observables, based on different physics, are tracking

13440-491: The Milne model , the oscillatory universe (originally suggested by Friedmann, but advocated by Albert Einstein and Richard C. Tolman ) and Fritz Zwicky 's tired light hypothesis. 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. The other

13632-439: The cosmological constant , which is associated with a vacuum energy or dark energy in empty space that is used to explain the contemporary accelerating expansion of space against the attractive effects of gravity. A cosmological constant has negative pressure, p = − ρ c 2 {\displaystyle p=-\rho c^{2}} , which contributes to the stress–energy tensor that, according to

13824-488: 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. Inflation and baryogenesis remain more speculative features of current Big Bang models. Viable, quantitative explanations for such phenomena are still being sought. These are unsolved problems in physics. Observations of distant galaxies and quasars show that these objects are redshifted:

14016-682: The field equation for gravity relates this tensor and the Ricci tensor , which describes a particular class of tidal effects: the change in volume for a small cloud of test particles that are initially at rest, and then fall freely. In special relativity, conservation of energy –momentum corresponds to the statement that the energy–momentum tensor is divergence -free. This formula, too, is readily generalized to curved spacetime by replacing partial derivatives with their curved- manifold counterparts, covariant derivatives studied in differential geometry. With this additional condition—the covariant divergence of

14208-472: The general theory of relativity , and as Einstein's theory of gravity , is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics . General relativity generalizes special relativity and refines Newton's law of universal gravitation , providing a unified description of gravity as a geometric property of space and time , or four-dimensional spacetime . In particular,

14400-473: The post-Newtonian expansion , both of which were developed by Einstein. The latter provides a systematic approach to solving for the geometry of a spacetime that contains a distribution of matter that moves slowly compared with the speed of light. The expansion involves a series of terms; the first terms represent Newtonian gravity, whereas the later terms represent ever smaller corrections to Newton's theory due to general relativity. An extension of this expansion

14592-454: The scalar gravitational potential of classical physics by a symmetric rank -two tensor , the latter reduces to the former in certain limiting cases . For weak gravitational fields and slow speed relative to the speed of light, the theory's predictions converge on those of Newton's law of universal gravitation. As it is constructed using tensors, general relativity exhibits general covariance : its laws—and further laws formulated within

14784-429: The summation convention is used for repeated indices α {\displaystyle \alpha } and β {\displaystyle \beta } . The quantity on the left-hand-side of this equation is the acceleration of a particle, and so this equation is analogous to Newton's laws of motion which likewise provide formulae for the acceleration of a particle. This equation of motion employs

14976-484: The universe expanded from an initial state of high density and temperature . The notion of an expanding universe was first scientifically originated by physicist Alexander Friedmann in 1922 with the mathematical derivation of the Friedmann equations . The earliest empirical observation of the notion of an expanding universe is known as Hubble's Law , published in work by physicist Edwin Hubble in 1929, which discerned that galaxies are moving away from Earth at

15168-410: The "four pillars" of the Big Bang models. 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 the subject of most active laboratory investigations. Remaining issues include the cuspy halo problem and

15360-430: The 1980s, most research focused on cold dark matter with critical density in matter, around 95 % CDM and 5 % baryons: these showed success at forming galaxies and clusters of galaxies, but problems remained; notably, the model required a Hubble constant lower than preferred by observations, and observations around 1988–1990 showed more large-scale galaxy clustering than predicted. These difficulties sharpened with

15552-533: The Big Bang. Then, from the 1970s to the 1990s, cosmologists worked on characterizing the features of the Big Bang universe and resolving outstanding problems. In 1981, Alan Guth made a breakthrough in theoretical work on resolving certain outstanding theoretical problems in the Big Bang models with the introduction of an epoch of rapid expansion in the early universe he called "inflation". Meanwhile, during these decades, two questions in observational cosmology that generated much discussion and disagreement were over

15744-462: The Big Bang. Since the early universe did not immediately collapse into a multitude of black holes, matter at that time must have been very evenly distributed with a negligible density gradient . The earliest phases of the Big Bang are subject to much speculation, given the lack of available data. In the most common models the universe was filled homogeneously and isotropically with a very high energy density and huge temperatures and pressures , and

15936-464: The CMB are, in fact, statistically significant and can no longer be ignored. Already in 1967, Dennis Sciama predicted that the cosmic microwave background has a significant dipole anisotropy. In recent years, the CMB dipole has been tested, and the results suggest our motion with respect to distant radio galaxies and quasars differs from our motion with respect to the cosmic microwave background . The same conclusion has been reached in recent studies of

16128-615: The CMB dipole direction suggests that the Universe is anisotropic in the direction of the CMB dipole. Nevertheless, some authors have stated that the universe around Earth is isotropic at high significance by studies of the cosmic microwave background temperature maps. Based on N-body simulations in ΛCDM, Yadav and his colleagues showed that the spatial distribution of galaxies is statistically homogeneous if averaged over scales 260 /h Mpc or more. However, many large-scale structures have been discovered, and some authors have reported some of

16320-602: The CMB, discovered in 2002 by DASI, has been successfully predicted by the model: in the 2015 Planck data release, there are seven observed peaks in the temperature (TT) power spectrum, six peaks in the temperature–polarization (TE) cross spectrum, and five peaks in the polarization (EE) spectrum. The six free parameters can be well constrained by the TT spectrum alone, and then the TE and EE spectra can be predicted theoretically to few-percent precision with no further adjustments allowed. Over

16512-442: The Hubble constant based on the cosmic background radiation compared to astronomical distance measurements. This difference has been called the Hubble tension . The Hubble tension in cosmology is widely acknowledged to be a major problem for the ΛCDM model. In December 2021, National Geographic reported that the cause of the Hubble tension discrepancy is not known. However, if the cosmological principle fails (see Violations of

16704-513: The Hubble constant. However, other work has found no evidence for this in observations, finding the scale of the claimed underdensity to be incompatible with observations which extend beyond its radius. Important deficiencies were subsequently pointed out in this analysis, leaving open the possibility that the Hubble tension is indeed caused by outflow from the KBC void. As a result of the Hubble tension, other researchers have called for new physics beyond

16896-482: The Newtonian limit and treating the orbiting body as a test particle . For him, the fact that his theory gave a straightforward explanation of Mercury's anomalous perihelion shift, discovered earlier by Urbain Le Verrier in 1859, was important evidence that he had at last identified the correct form of the gravitational field equations. Big Bang The Big Bang is a physical theory that describes how

17088-464: The absence of a perfect cosmological principle , 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. This irregular behavior, known as the gravitational singularity , indicates that general relativity is not an adequate description of the laws of physics in this regime. Models based on general relativity alone cannot fully extrapolate toward

17280-413: The actual motions of bodies and making allowances for the external forces (such as electromagnetism or friction ), can be used to define the geometry of space, as well as a time coordinate . However, there is an ambiguity once gravity comes into play. According to Newton's law of gravity, and independently verified by experiments such as that of Eötvös and its successors (see Eötvös experiment ), there

17472-508: The age measured today). This issue was later resolved when new computer simulations, which included the effects of mass loss due to stellar winds , indicated a much younger age for globular clusters. Significant progress in Big Bang cosmology has 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 the Cosmic Background Explorer (COBE),

17664-401: The base of cosmological models of an expanding universe . Widely acknowledged as a theory of extraordinary beauty , general relativity has often been described as the most beautiful of all existing physical theories. Henri Poincaré 's 1905 theory of the dynamics of the electron was a relativistic theory which he applied to all forces, including gravity. While others thought that gravity

17856-411: The big-bang predictions by Alpher, Herman and Gamow around 1950. Through the 1970s, the radiation was found to be approximately consistent with a blackbody 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

18048-403: The birth of the universe), defined relative to the present time, so a 0 = a ( t 0 ) = 1 {\displaystyle a_{0}=a(t_{0})=1} ; the usual convention in cosmology is that subscript 0 denotes present-day values, so t 0 {\displaystyle t_{0}} denotes the age of the universe. The scale factor is related to

18240-535: The collision velocity leads to strong ( 6.16 σ {\displaystyle 6.16\sigma } ) tension with the ΛCDM model. The properties of El Gordo are however consistent with cosmological simulations in the framework of MOND due to more rapid structure formation. The KBC void is an immense, comparatively empty region of space containing the Milky Way approximately 2 billion light-years (600 megaparsecs, Mpc) in diameter. Some authors have said

18432-406: The connection that satisfies the equivalence principle and makes space locally Minkowskian (that is, in suitable locally inertial coordinates , the metric is Minkowskian, and its first partial derivatives and the connection coefficients vanish). Having formulated the relativistic, geometric version of the effects of gravity, the question of gravity's source remains. In Newtonian gravity, the source

18624-432: The corresponding neutrino density Ω v h 2 {\displaystyle \Omega _{\text{v}}h^{2}} is estimated to be less than 0.0062. 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 appears to homogeneously permeate all of space. Observations suggest that 73% of

18816-415: The cosmological parameters, which can then be compared with observations such as supernovae and baryon acoustic oscillations . In the minimal 6-parameter Lambda-CDM model, it is assumed that curvature Ω k {\displaystyle \Omega _{k}} is zero and w = − 1 {\displaystyle w=-1} , so this simplifies to Observations show that

19008-472: The cosmological principle ), then the existing interpretations of the Hubble constant and the Hubble tension have to be revised, which might resolve the Hubble tension. Some authors postulate that the Hubble tension can be explained entirely by the KBC void , as measuring galactic supernovae inside a void is predicted by the authors to yield a larger local value for the Hubble constant than cosmological measures of

19200-391: The critical density; though other outcomes are possible in extended models where the dark energy is not constant but actually time-dependent. It is standard to define the present-day density parameter Ω x {\displaystyle \Omega _{x}} for various species as the dimensionless ratio where the subscript x {\displaystyle x}

19392-560: The deflection of starlight by the Sun during the total solar eclipse of 29 May 1919 , instantly making Einstein famous. Yet the theory remained outside the mainstream of theoretical physics and astrophysics until developments between approximately 1960 and 1975, now known as the golden age of general relativity . Physicists began to understand the concept of a black hole, and to identify quasars as one of these objects' astrophysical manifestations. Ever more precise solar system tests confirmed

19584-452: The determination of the Hubble constant is known as Hubble tension . Techniques based on observation of the CMB suggest a lower value of this constant compared to the quantity derived from measurements based on the cosmic distance ladder. In 1964, Arno Penzias and Robert Wilson serendipitously discovered the cosmic background radiation, an omnidirectional signal in the microwave band. Their discovery provided substantial confirmation of

19776-495: The discovery of CMB anisotropy by the Cosmic Background Explorer in 1992, and several modified CDM models, including ΛCDM and mixed cold and hot dark matter, came under active consideration through the mid-1990s. The ΛCDM model then became the leading model following the observations of accelerating expansion in 1998, and was quickly supported by other observations: in 2000, the BOOMERanG microwave background experiment measured

19968-452: The emission of gravitational waves and effects related to the relativity of direction. In general relativity, the apsides of any orbit (the point of the orbiting body's closest approach to the system's center of mass ) will precess ; the orbit is not an ellipse , but akin to an ellipse that rotates on its focus, resulting in a rose curve -like shape (see image). Einstein first derived this result by using an approximate metric representing

20160-500: The end-state for massive stars . Microquasars and active galactic nuclei are believed to be stellar black holes and supermassive black holes . It also predicts gravitational lensing , where the bending of light results in multiple images of the same distant astronomical phenomenon. Other predictions include the existence of gravitational waves , which have been observed directly by the physics collaboration LIGO and other observatories. In addition, general relativity has provided

20352-555: The energy–momentum tensor, and hence of whatever is on the other side of the equation, is zero—the simplest nontrivial set of equations are what are called Einstein's (field) equations: G μ ν ≡ R μ ν − 1 2 R g μ ν = κ T μ ν {\displaystyle G_{\mu \nu }\equiv R_{\mu \nu }-{\textstyle 1 \over 2}R\,g_{\mu \nu }=\kappa T_{\mu \nu }\,} On

20544-478: The enhanced clustering of galaxies) that cannot be accounted for by the quantity of observed matter. The ΛCDM model proposes specifically cold dark matter , hypothesized as: Dark matter constitutes about 26.5 % of the mass–energy density of the universe. The remaining 4.9 % comprises all ordinary matter observed as atoms, chemical elements, gas and plasma, the stuff of which visible planets, stars and galaxies are made. The great majority of ordinary matter in

20736-446: The equivalence principle holds, gravity influences the passage of time. Light sent down into a gravity well is blueshifted , whereas light sent in the opposite direction (i.e., climbing out of the gravity well) is redshifted ; collectively, these two effects are known as the gravitational frequency shift. More generally, processes close to a massive body run more slowly when compared with processes taking place farther away; this effect

20928-456: The exceedingly weak waves that are expected to arrive here on Earth from far-off cosmic events, which typically result in relative distances increasing and decreasing by 10 − 21 {\displaystyle 10^{-21}} or less. Data analysis methods routinely make use of the fact that these linearized waves can be Fourier decomposed . Some exact solutions describe gravitational waves without any approximation, e.g.,

21120-440: The existence of the KBC void violates the assumption that the CMB reflects baryonic density fluctuations at z = 1100 {\displaystyle z=1100} or Einstein's theory of general relativity , either of which would violate the ΛCDM model, while other authors have claimed that supervoids as large as the KBC void are consistent with the ΛCDM model. Statistically significant differences remain in measurements of

21312-591: The expansion using Type Ia supernovae and measurements of temperature fluctuations in the cosmic microwave background, the time that has passed since that event—known as the " age of the universe "—is 13.8 billion years. Despite being extremely dense at this time—far denser than is usually required to form a black hole —the universe did not re-collapse into a singularity. Commonly used calculations and limits for explaining gravitational collapse are usually based upon objects of relatively constant size, such as stars, and do not apply to rapidly expanding space such as

21504-400: The expansion, a phase transition caused a cosmic inflation , during which the universe grew exponentially , unconstrained by the light speed invariance , and temperatures dropped by a factor of 100,000. This concept is motivated by the flatness problem , where the density of matter and energy is very close to the critical density needed to produce a flat universe . That is, the shape of

21696-408: The exterior Schwarzschild solution or, for more than a single mass, the post-Newtonian expansion), several effects of gravity on light propagation emerge. Although the bending of light can also be derived by extending the universality of free fall to light, the angle of deflection resulting from such calculations is only half the value given by general relativity. Closely related to light deflection

21888-415: 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 . Ten years later, Alexander Friedmann ,

22080-433: The first non-trivial exact solution to the Einstein field equations, the Schwarzschild metric . This solution laid the groundwork for the description of the final stages of gravitational collapse, and the objects known today as black holes. In the same year, the first steps towards generalizing Schwarzschild's solution to electrically charged objects were taken, eventually resulting in the Reissner–Nordström solution , which

22272-412: The general relativistic framework—take on the same form in all coordinate systems . Furthermore, the theory does not contain any invariant geometric background structures, i.e. it is background independent . It thus satisfies a more stringent general principle of relativity , namely that the laws of physics are the same for all observers. Locally , as expressed in the equivalence principle, spacetime

22464-485: The general theory of relativity, causes accelerating expansion. The fraction of the total energy density of our (flat or almost flat) universe that is dark energy, Ω Λ {\displaystyle \Omega _{\Lambda }} , is estimated to be 0.669 ± 0.038 based on the 2018 Dark Energy Survey results using Type Ia supernovae or 0.6847 ± 0.0073 based on the 2018 release of Planck satellite data, or more than 68.3 % (2018 estimate) of

22656-484: The geometry of space. Predicted in 1916 by Albert Einstein, there are gravitational waves: ripples in the metric of spacetime that propagate at the speed of light. These are one of several analogies between weak-field gravity and electromagnetism in that, they are analogous to electromagnetic waves . On 11 February 2016, the Advanced LIGO team announced that they had directly detected gravitational waves from

22848-404: The gravitational effects of an unknown dark matter surrounding galaxies. Most of the gravitational potential in the universe seems to be in this form, and the Big Bang models and various observations indicate that this excess gravitational potential is not created by baryonic matter , such as normal atoms. Measurements of the redshifts of supernovae indicate that the expansion of the universe

23040-414: The history of the universe and have provided the modern framework for cosmology , thus leading to the discovery of the Big Bang and cosmic microwave background radiation. Despite the introduction of a number of alternative theories , general relativity continues to be the simplest theory consistent with experimental data . Reconciliation of general relativity with the laws of quantum physics remains

23232-441: The image), and a set of events for which such an influence is impossible (such as event C in the image). These sets are observer -independent. In conjunction with the world-lines of freely falling particles, the light-cones can be used to reconstruct the spacetime's semi-Riemannian metric, at least up to a positive scalar factor. In mathematical terms, this defines a conformal structure or conformal geometry. Special relativity

23424-446: The influence of the gravitational force. This suggests the definition of a new class of inertial motion, namely that of objects in free fall under the influence of gravity. This new class of preferred motions, too, defines a geometry of space and time—in mathematical terms, it is the geodesic motion associated with a specific connection which depends on the gradient of the gravitational potential . Space, in this construction, still has

23616-417: The key mathematical framework on which he fit his physical ideas of gravity. This idea was pointed out by mathematician Marcel Grossmann and published by Grossmann and Einstein in 1913. The Einstein field equations are nonlinear and considered difficult to solve. Einstein used approximation methods in working out initial predictions of the theory. But in 1916, the astrophysicist Karl Schwarzschild found

23808-440: The known laws of physics , the models describe an increasingly concentrated cosmos preceded by a singularity in which space and time lose meaning (typically named "the Big Bang singularity"). Physics lacks a widely accepted theory of quantum gravity that can model the earliest conditions of the Big Bang. In 1964 the CMB was discovered, which convinced many cosmologists that the competing steady-state model of cosmic evolution

24000-411: The lambda-CDM model of cosmology, which uses the independent frameworks of quantum mechanics and general relativity. There are no easily testable models that would describe the situation prior to approximately 10 seconds. Understanding this earliest of eras in the history of the universe is one of the greatest unsolved problems in physics . English astronomer Fred Hoyle is credited with coining

24192-410: The language of spacetime: the straight time-like lines that define a gravity-free inertial frame are deformed to lines that are curved relative to each other, suggesting that the inclusion of gravity necessitates a change in spacetime geometry. A priori, it is not clear whether the new local frames in free fall coincide with the reference frames in which the laws of special relativity hold—that theory

24384-493: The largest possible deviation of the fine-structure constant over much of the age of the universe is of order 10 . Also, general relativity has passed stringent tests on the scale of the Solar System and binary stars . The large-scale universe appears isotropic as viewed from Earth. If it is indeed isotropic, the cosmological principle can be derived from the simpler Copernican principle , which states that there

24576-457: The left-hand side is the Einstein tensor , G μ ν {\displaystyle G_{\mu \nu }} , which is symmetric and a specific divergence-free combination of the Ricci tensor R μ ν {\displaystyle R_{\mu \nu }} and the metric. In particular, is the curvature scalar. The Ricci tensor itself is related to

24768-405: 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 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

24960-477: The light of stars or distant quasars being deflected as it passes the Sun . This and related predictions follow from the fact that light follows what is called a light-like or null geodesic —a generalization of the straight lines along which light travels in classical physics. Such geodesics are the generalization of the invariance of lightspeed in special relativity. As one examines suitable model spacetimes (either

25152-399: The mass–energy density of the universe. Dark matter is postulated in order to account for gravitational effects observed in very large-scale structures (the "non-keplerian" rotation curves of galaxies; the gravitational lensing of light by galaxy clusters; and

25344-455: The matter's energy–momentum tensor must be divergence-free. The matter must, of course, also satisfy whatever additional equations were imposed on its properties. In short, such a solution is a model universe that satisfies the laws of general relativity, and possibly additional laws governing whatever matter might be present. Einstein's equations are nonlinear partial differential equations and, as such, difficult to solve exactly. Nevertheless,

25536-438: The model and pin down the parameter values, most of which are constrained below 1 percent uncertainty. Research is active into many aspects of the ΛCDM model, both to refine the parameters and to resolve the tensions between recent observations and the ΛCDM model, such as the Hubble tension and the CMB dipole . In addition, ΛCDM has no explicit physical theory for the origin or physical nature of dark matter or dark energy;

25728-442: The more general Riemann curvature tensor as On the right-hand side, κ {\displaystyle \kappa } is a constant and T μ ν {\displaystyle T_{\mu \nu }} is the energy–momentum tensor. All tensors are written in abstract index notation . Matching the theory's prediction to observational results for planetary orbits or, equivalently, assuring that

25920-460: The nearly scale-invariant spectrum of the CMB perturbations, and their image across the celestial sphere, are believed to result from very small thermal and acoustic irregularities at the point of recombination. Historically, a large majority of astronomers and astrophysicists support the ΛCDM model or close relatives of it, but recent observations that contradict the ΛCDM model have led some astronomers and astrophysicists to search for alternatives to

26112-453: 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. During the 1930s, other ideas were proposed as non-standard cosmologies to explain Hubble's observations, including

26304-483: The observable particle horizon . The model uses the Friedmann–Lemaître–Robertson–Walker metric , the Friedmann equations , and the cosmological equations of state to describe the observable universe from approximately 0.1 s to the present. The expansion of the universe is parameterized by a dimensionless scale factor a = a ( t ) {\displaystyle a=a(t)} (with time t {\displaystyle t} counted from

26496-432: The observation of binary pulsars . All results are in agreement with general relativity. However, at the current level of accuracy, these observations cannot distinguish between general relativity and other theories in which the equivalence principle is valid. General relativity predicts that the path of light will follow the curvature of spacetime as it passes near a star. This effect was initially confirmed by observing

26688-460: The observational evidence, most notably from radio source counts , began to favor Big Bang over steady state. The discovery and confirmation of the CMB in 1964 secured the Big Bang as the best theory of the origin and evolution of the universe. In 1968 and 1970, Roger Penrose , Stephen Hawking , and George F. R. Ellis published papers where they showed that mathematical singularities were an inevitable initial condition of relativistic models of

26880-417: The observed redshift z {\displaystyle z} of the light emitted at time t e m {\displaystyle t_{\mathrm {em} }} by The expansion rate is described by the time-dependent Hubble parameter , H ( t ) {\displaystyle H(t)} , defined as where a ˙ {\displaystyle {\dot {a}}}

27072-482: 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. Some processes in the early universe occurred too slowly, compared to the expansion rate of the universe, to reach approximate thermodynamic equilibrium . Others were fast enough to reach thermalization . The parameter usually used to find out whether

27264-459: The ordinary Euclidean geometry . However, space time as a whole is more complicated. As can be shown using simple thought experiments following the free-fall trajectories of different test particles, the result of transporting spacetime vectors that can denote a particle's velocity (time-like vectors) will vary with the particle's trajectory; mathematically speaking, the Newtonian connection is not integrable . From this, one can deduce that spacetime

27456-404: The original matter particles 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

27648-529: The other astronomical structures observable today. 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 (CDM), warm dark matter , hot dark matter , and baryonic matter . The best measurements available, from the Wilkinson Microwave Anisotropy Probe (WMAP), show that the data is well-fit by a Lambda-CDM model in which dark matter

27840-469: The other forces, with only the electromagnetic force and weak nuclear force remaining unified. Inflation stopped locally at around 10 to 10 seconds, with the observable universe's volume having increased by a factor of at least 10 . Reheating followed as the inflaton field decayed, until the universe obtained the temperatures required for the production of a quark–gluon plasma as well as all other elementary particles . Temperatures were so high that

28032-502: The passage of time, the geometry of space, the motion of bodies in free fall , and the propagation of light, and include gravitational time dilation , gravitational lensing , the gravitational redshift of light, the Shapiro time delay and singularities / black holes . So far, all tests of general relativity have been shown to be in agreement with the theory. The time-dependent solutions of general relativity enable us to talk about

28224-427: 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. 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

28416-512: The photon radiation . The recombination epoch began after about 379,000 years, when the electrons and nuclei combined into atoms (mostly hydrogen ), which were able to emit radiation. This relic radiation, which continued through space largely unimpeded, is known as the cosmic microwave background. After the recombination epoch, the slightly denser regions of the uniformly distributed matter gravitationally attracted nearby matter and thus grew even denser, forming gas clouds, stars, galaxies, and

28608-506: The picture becomes less speculative, since particle energies drop to values that can be attained in particle accelerators . At about 10 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 no longer high enough to create either new proton–antiproton or neutron–antineutron pairs. A mass annihilation immediately followed, leaving just one in 10 of

28800-488: The precise values of the Hubble Constant and the matter-density of the universe (before the discovery of dark energy, thought to be the key predictor for the eventual fate of the universe ). In the mid-1990s, observations of certain globular clusters appeared to indicate that they were about 15 billion years old, which conflicted with most then-current estimates of the age of the universe (and indeed with

28992-440: The predecessors of the ΛCDM model were being developed, there was not sufficient data available to distinguish between more complex anisotropic or inhomogeneous models, so homogeneity and isotropy were assumed to simplify the models, and the assumptions were carried over into the ΛCDM model. However, recent findings have suggested that violations of the cosmological principle, especially of isotropy, exist. These violations have called

29184-461: The predominance of matter over antimatter in the present universe. 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, with the electromagnetic force and weak nuclear force separating at about 10 seconds. After about 10 seconds,

29376-511: The preface to Relativity: The Special and the General Theory , Einstein said "The present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics. The work presumes a standard of education corresponding to that of

29568-430: The principle of equivalence and his sense that a proper description of gravity should be geometrical at its basis, so that there was an "element of revelation" in the manner in which Einstein arrived at his theory. Other elements of beauty associated with the general theory of relativity are its simplicity and symmetry, the manner in which it incorporates invariance and unification, and its perfect logical consistency. In

29760-505: The radiation density is very small today, Ω rad ∼ 10 − 4 {\displaystyle \Omega _{\text{rad}}\sim 10^{-4}} ; if this term is neglected the above has an analytic solution where t Λ ≡ 2 / ( 3 H 0 Ω Λ )   ; {\displaystyle t_{\Lambda }\equiv 2/(3H_{0}{\sqrt {\Omega _{\Lambda }}})\ ;} this

29952-427: The random motions of particles were at relativistic speeds , and particle–antiparticle pairs of all kinds were being continuously created and destroyed in collisions. 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

30144-467: The reduced Hubble constant. If the cosmological constant were actually zero, the critical density would also mark the dividing line between eventual recollapse of the universe to a Big Crunch , or unlimited expansion. For the Lambda-CDM model with a positive cosmological constant (as observed), the universe is predicted to expand forever regardless of whether the total density is slightly above or below

30336-446: The same premises, which include additional rules and/or constraints, leading to different field equations. Examples are Whitehead's theory , Brans–Dicke theory , teleparallelism , f ( R ) gravity and Einstein–Cartan theory . The derivation outlined in the previous section contains all the information needed to define general relativity, describe its key properties, and address a question of crucial importance in physics, namely how

30528-410: The singularity. In some proposals, such as the emergent Universe models, the singularity is replaced by another cosmological epoch. A different approach identifies the initial singularity as a singularity predicted by some models of the Big Bang theory to have existed before the Big Bang event. This primordial singularity is itself sometimes called "the Big Bang", but the term can also refer to

30720-495: The size of the observable universe , the Hubble redshift can be thought of as the Doppler shift corresponding to the recession velocity v {\displaystyle v} . For distances comparable to the size of the observable universe, the attribution of the cosmological redshift becomes more ambiguous, although its interpretation as a kinematic Doppler shift remains the most natural one. An unexplained discrepancy with

30912-408: The size of the objects (e.g. galaxies) in space. Also since it originates from ordinary general relativity, it, like general relativity, allows for distant galaxies to recede from each other at speeds greater than the speed of light; local expansion is less than the speed of light, but expansion summed across great distances can collectively exceed the speed of light. The letter Λ ( lambda ) represents

31104-472: The speed of light in vacuum. When there is no matter present, so that the energy–momentum tensor vanishes, the results are the vacuum Einstein equations, In general relativity, the world line of a particle free from all external, non-gravitational force is a particular type of geodesic in curved spacetime. In other words, a freely moving or falling particle always moves along a geodesic. The geodesic equation is: where s {\displaystyle s}

31296-406: The steady-state theory. This perception was enhanced by the fact that the originator of the Big Bang concept, Lemaître, was a Roman Catholic priest. 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. Lemaître, however, disagreed: If the world has begun with a single quantum ,

31488-492: The structures to be in conflict with the predicted scale of homogeneity for ΛCDM, including Other authors claim that the existence of structures larger than the scale of homogeneity in the ΛCDM model does not necessarily violate the cosmological principle in the ΛCDM model. El Gordo is a massive interacting galaxy cluster in the early Universe ( z = 0.87 {\displaystyle z=0.87} ). The extreme properties of El Gordo in terms of its redshift, mass, and

31680-447: The temperature was about a billion kelvin and the density of matter in the universe was comparable to the current density of Earth's atmosphere, neutrons combined with protons to form the universe's deuterium and helium nuclei in a process called Big Bang nucleosynthesis (BBN). Most protons remained uncombined as hydrogen nuclei. As the universe cooled, the rest energy density of matter came to gravitationally dominate that of

31872-465: The term "Big Bang" during a talk for a March 1949 BBC Radio broadcast, saying: "These theories were based on the hypothesis that all the matter in the universe was created in one big bang at a particular time in the remote past." However, it did not catch on until the 1970s. 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

32064-518: The theory can be used for model-building. General relativity is a metric theory of gravitation. At its core are Einstein's equations , which describe the relation between the geometry of a four-dimensional pseudo-Riemannian manifold representing spacetime, and the energy–momentum contained in that spacetime. Phenomena that in classical mechanics are ascribed to the action of the force of gravity (such as free-fall , orbital motion, and spacecraft trajectories ), correspond to inertial motion within

32256-644: The theory's predictive power, and relativistic cosmology also became amenable to direct observational tests. General relativity has acquired a reputation as a theory of extraordinary beauty. Subrahmanyan Chandrasekhar has noted that at multiple levels, general relativity exhibits what Francis Bacon has termed a "strangeness in the proportion" ( i.e . elements that excite wonderment and surprise). It juxtaposes fundamental concepts (space and time versus matter and motion) which had previously been considered as entirely independent. Chandrasekhar also noted that Einstein's only guides in his search for an exact theory were

32448-405: The total (matter–energy) density to be close to 100 % of critical, whereas in 2001 the 2dFGRS galaxy redshift survey measured the matter density to be near 25 %; the large difference between these values supports a positive Λ or dark energy . Much more precise spacecraft measurements of the microwave background from WMAP in 2003–2010 and Planck in 2013–2015 have continued to support

32640-452: The total energy density of the present day universe is in this form. When the universe was very young it was likely infused with dark energy, but with everything closer together, gravity predominated, braking the expansion. Eventually, after billions of years of expansion, the declining density of matter relative to the density of dark energy allowed the expansion of the universe to begin to accelerate. Dark energy in its simplest formulation

32832-408: The transition from decelerating to accelerating expansion (the second derivative a ¨ {\displaystyle {\ddot {a}}} crossing zero) occurred when which evaluates to a ∼ 0.6 {\displaystyle a\sim 0.6} or z ∼ 0.66 {\displaystyle z\sim 0.66} for the best-fit parameters estimated from

33024-487: The two become significant when dealing with speeds approaching the speed of light , and with high-energy phenomena. With Lorentz symmetry, additional structures come into play. They are defined by the set of light cones (see image). The light-cones define a causal structure: for each event A , there is a set of events that can, in principle, either influence or be influenced by A via signals or interactions that do not need to travel faster than light (such as event B in

33216-416: The universe has no overall geometric curvature due to gravitational influence. Microscopic quantum fluctuations that occurred because of Heisenberg's uncertainty principle were "frozen in" by inflation, becoming amplified into the seeds that would later form the large-scale structure of the universe. At a time around 10 seconds, the electroweak epoch begins when the strong nuclear force separates from

33408-422: The universe has a finite age, and light travels at a finite speed, there may be events in the past whose light has not yet had time to reach earth. 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

33600-489: The universe is expanding. This is readily described by the expanding cosmological solutions found by Friedmann in 1922, which do not require a cosmological constant. Lemaître used these solutions to formulate the earliest version of the Big Bang models, in which the universe has evolved from an extremely hot and dense earlier state. Einstein later declared the cosmological constant the biggest blunder of his life. During that period, general relativity remained something of

33792-490: The universe is uniformly expanding everywhere. This cosmic expansion was predicted from general relativity by Friedmann in 1922 and Lemaître in 1927, well before Hubble made his 1929 analysis and observations, and it remains the cornerstone of the Big Bang model as developed by Friedmann, Lemaître, Robertson, and Walker. The theory requires the relation v = H D {\displaystyle v=HD} to hold at all times, where D {\displaystyle D}

33984-400: The universe is unseen, since visible stars and gas inside galaxies and clusters account for less than 10 % of the ordinary matter contribution to the mass–energy density of the universe. The model includes a single originating event, the " Big Bang ", which was not an explosion but the abrupt appearance of expanding spacetime containing radiation at temperatures of around 10 K. This

34176-449: 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 (BBN). More recent evidence includes observations of galaxy formation and evolution , and the distribution of large-scale cosmic structures . These are sometimes called

34368-494: The weak-gravity, low-speed limit is Newtonian mechanics, the proportionality constant κ {\displaystyle \kappa } is found to be κ = 8 π G c 4 {\textstyle \kappa ={\frac {8\pi G}{c^{4}}}} , where G {\displaystyle G} is the Newtonian constant of gravitation and c {\displaystyle c}

34560-416: The years, numerous simulations of ΛCDM and observations of our universe have been made that challenge the validity of the ΛCDM model, to the point where some cosmologists believe that the ΛCDM model may be superseded by a different, as yet unknown cosmological model. Extensive searches for dark matter particles have so far shown no well-agreed detection, while dark energy may be almost impossible to detect in

34752-474: The ΛCDM model into question, with some authors suggesting that the cosmological principle is obsolete or that the Friedmann–Lemaître–Robertson–Walker metric breaks down in the late universe. This has additional implications for the validity of the cosmological constant in the ΛCDM model, as dark energy is implied by observations only if the cosmological principle is true. Evidence from galaxy clusters , quasars , and type Ia supernovae suggest that isotropy

34944-591: The ΛCDM model may be incomplete or in need of correction. Some values for S 8 {\displaystyle S_{8}} are 0.832 ± 0.013 (2020 Planck ), 0.766 +0.020 −0.014 (2021 KIDS ), 0.776 ± 0.017 (2022 DES ), 0.790 +0.018 −0.014 (2023 DES+KIDS), 0.769 +0.031 −0.034 – 0.776 +0.032 −0.033 (2023 HSC-SSP ), 0.86 ± 0.01 (2024 EROSITA ). Values have also obtained using peculiar velocities , 0.637 ± 0.054 (2020) and 0.776 ± 0.033 (2020), among other methods. General relativity General relativity , also known as

35136-521: The ΛCDM model quantifies the amplitude of matter fluctuations in the late universe and is defined as Early- (e.g. from CMB data collected using the Planck observatory) and late-time (e.g. measuring weak gravitational lensing events) facilitate increasingly precise values of S 8 {\displaystyle S_{8}} . However, these two categories of measurement differ by more standard deviations than their uncertainties. This discrepancy

35328-409: The ΛCDM model, which include dropping the Friedmann–Lemaître–Robertson–Walker metric or modifying dark energy . On the other hand, Milgrom , McGaugh , and Kroupa have long been leading critics of the ΛCDM model, attacking the dark matter portions of the theory from the perspective of galaxy formation models and supporting the alternative modified Newtonian dynamics (MOND) theory, which requires

35520-435: The ΛCDM model. Moritz Haslbauer et al. proposed that MOND would resolve the Hubble tension. Another group of researchers led by Marc Kamionkowski proposed a cosmological model with early dark energy to replace ΛCDM. The S 8 {\displaystyle S_{8}} tension in cosmology is another major problem for the ΛCDM model. The S 8 {\displaystyle S_{8}} parameter in

35712-422: Was falsified , since the Big Bang models predict a uniform background radiation caused by high temperatures and densities in the distant past. A wide range of empirical evidence strongly favors the Big Bang event, which is now essentially universally accepted. Detailed measurements of the expansion rate of the universe place the Big Bang singularity at an estimated 13.787 ± 0.020   billion years ago, which

35904-477: Was Lemaître's Big Bang theory, advocated and developed by George Gamow , who introduced BBN and whose associates, Ralph Alpher and Robert Herman , predicted the CMB. 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. For a while, support was split between these two theories. Eventually,

36096-455: Was immediately (within 10 seconds) followed by an exponential expansion of space by a scale multiplier of 10 or more, known as cosmic inflation . The early universe remained hot (above 10 000 K) for several hundred thousand years, a state that is detectable as a residual cosmic microwave background , or CMB, a very low-energy radiation emanating from all parts of the sky. The "Big Bang" scenario, with cosmic inflation and standard particle physics,

36288-474: Was instantaneous or of electromagnetic origin, he suggested that relativity was "something due to our methods of measurement". In his theory, he showed that gravitational waves propagate at the speed of light. Soon afterwards, Einstein started thinking about how to incorporate gravity into his relativistic framework. In 1907, beginning with a simple thought experiment involving an observer in free fall (FFO), he embarked on what would be an eight-year search for

36480-411: Was just a striking image meant to highlight the difference between the two models. Helge Kragh writes that the evidence for the claim that it was meant as a pejorative is "unconvincing", and mentions a number of indications that it was not a pejorative. The term itself has been argued to be a misnomer because it evokes an explosion. The argument is that whereas an explosion suggests expansion into

36672-452: Was no consensus on the makeup of the energy density of the universe. Some alternative models challenge the assumptions of the ΛCDM model. Examples of these are modified Newtonian dynamics , entropic gravity , modified gravity, theories of large-scale variations in the matter density of the universe, bimetric gravity , scale invariance of empty space, and decaying dark matter (DDM). The ΛCDM model includes an expansion of metric space that

36864-478: Was very rapidly expanding and cooling. The period up to 10 seconds into the expansion, the Planck epoch , was a phase in which the four fundamental forces —the electromagnetic force , the strong nuclear force , the weak nuclear force , and the gravitational force , were unified as one. In this stage, the characteristic scale length of the universe was the Planck length , 1.6 × 10  m , and consequently had

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