| Physical cosmology | | | | Related topics | | | | edit Cosmology, as a branch of astrophysics, is the study of the universe on the largest scales and at the earliest times. ...
Download high resolution version (2198x1274, 1278 KB)WMAP map of CMB anisotropy This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ...
The age of the Universe is defined as the largest possible value of proper time integrated along a timelike curve from the Earth at the present epoch back to the Big Bang. ...
According to the Big Bang theory, the universe originated in an extremely dense and hot state (bottom). ...
Cosmic microwave background radiation - Wikipedia, the free encyclopedia /**/ @import /skins-1. ...
In cosmology, dark energy is a hypothetical form of energy which permeates all of space and has strong negative pressure. ...
In cosmology, dark matter consists of matter particles that cannot be detected by their emitted radiation but whose presence can be inferred from gravitational effects on visible matter such as stars and galaxies. ...
The Friedmann-Lemaître-Robertson-Walker (FLRW) metric describes a homogeneous, isotropic expanding/contracting universe. ...
The Friedmann equations relate various cosmological parameters within the context of general relativity. ...
In astrophysics, the questions of galaxy formation and evolution are: How, from a homogeneous universe, did we obtain the very inhomogeneous one we live in? How did galaxies form? How do galaxies change over time? The formation of galaxies is still one of the most active research areas in astrophysics...
Hubbles law is the statement in physical cosmology that the redshift in light coming from distant galaxies is proportional to their distance. ...
Astronomy and cosmology examine the universe to understand the large-scale structure of the cosmos. ...
ΛCDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter. ...
In cosmology, Big Bang nucleosynthesis refers to the process of element production during the early phases of the universe, shortly after the Big Bang. ...
Redshift describes a change in the wavelength of light, in which the wavelength is longer, or redder, than when it was emitted at the source. ...
The shape of the universe is a subject of investigation within cosmology. ...
The timeline of cosmology lists the sequence of cosmological theories and discoveries in chronological order. ...
It has been suggested that Timeline of the Big Bang be merged into this article or section. ...
The ultimate fate of the Universe is a subject of study in the field of cosmology. ...
Spiral Galaxy ESO 269-57 Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties (luminosity, density, temperature and chemical composition) of astronomical objects such as stars, galaxies, and the interstellar medium, as well as their interactions. ...
Two-dimensional visualization of space-time distortion. ...
Particles erupt from the collision point of two relativistic (100 GeV) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ...
Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ...
| The comoving distance or conformal distance of two objects in the universe is the distance divided by a time-varying scale factor representing the expansion of the universe. As a result the comoving distances on average are not increasing with time. The scale factor is usually taken to be one at present, so currently the comoving distance is equal to the ordinary distance. personal space, proxemics. ...
The scale factor, parameter of Friedmann-Lemaître-Robertson-Walker model, is a function of time which represents the relative expansion of the universe. ...
Thinking about the shape of the universe in the context of the standard Big Bang model is simplest using comoving coordinates. The shape of the universe is a subject of investigation within cosmology. ...
According to the Big Bang theory, the universe originated in an extremely dense and hot state (bottom). ...
See Cartesian coordinate system or Coordinates (elementary mathematics) for a more elementary introduction to this topic. ...
While special relativity states that all inertial reference frames are equivalent, i.e. that there is no favoured set of space-time coordinates, this is only a local theory. A simple introduction to this subject is provided in Special relativity for beginners Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein. ...
In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ...
General relativity is also a local theory, but it is used to constrain the local properties of a Riemannian manifold, which itself is global. Two-dimensional visualization of space-time distortion. ...
In Riemannian geometry, a Riemannian manifold is a real differentiable manifold in which each tangent space is equipped with an inner product in a manner which varies smoothly from point to point. ...
In the context of general relativity, the assumption of Weyl's postulate is that a favoured reference frame in space-time can be decided. The most common notion of such coordinates is that of comoving coordinates, where the spatial reference frame is attached to the average positions of galaxies (or any large lumps of matter which are at most moving slowly). Two-dimensional visualization of space-time distortion. ...
Weyls postulate states that the world lines of the galaxies form a three-bundle of non-intersecting geodesics orthonormal to a series of space-like hypersurfaces. ...
With this set of coordinates, both time and expansion of the Universe can be ignored in order to concentrate on the shape of space (formally speaking, of a spatial hypersurface at constant cosmological time). See Cartesian coordinate system or Coordinates (elementary mathematics) for a more elementary introduction to this topic. ...
The deepest visible-light image of the cosmos. ...
Space in comoving coordinates is (on average) static. This is perfectly consistent with the fact that the Universe is expanding. A choice of coordinates is just a choice of labels. There happens to be (according to the standard Big Bang model) a choice of these labels which can be used either for formal calculations or for intuition in which the Universe is static. To get back to thinking about an expanding Universe just requires remembering the scale factor. According to the Big Bang theory, the universe originated in an extremely dense and hot state (bottom). ...
The scale factor, parameter of Friedmann-Lemaître-Robertson-Walker model, is a function of time which represents the relative expansion of the universe. ...
This way there is also cosmological time, which for an observer at a fixed spatial point in comoving coordinates is identical to her local measurement of time.
Comoving distance is then the distance in comoving coordinates between two points in space, at a single cosmological time:
where a(t') is the scale factor. The scale factor, parameter of Friedmann-Lemaître-Robertson-Walker model, is a function of time which represents the relative expansion of the universe. ...
equivalent names
- Some textbooks use the symbol χ for comoving distance.
- proper distance is the name used by Weinberg (1972) [1] for comoving distance.
Is comoving distance a meaningless concept? Comoving distance and cosmological time definitely exist as part of the standard Big Bang model. However, while cosmological time is identical to locally measured time for an observer at a fixed comoving spatial position, the comoving distance is not, in the general case, identical to a distance as physically experienced by a particle moving slower than or at the speed of light. According to the Big Bang theory, the universe originated in an extremely dense and hot state (bottom). ...
Cherenkov effect in a swimming pool nuclear reactor. ...
If one divides a comoving distance by the present cosmological time (the age of the universe) and calls this a "velocity", then the resulting "velocities" of "galaxies" near the particle horizon or further than the horizon can be above the speed of light. This is the paradox of the ambiguous phrase space expanding faster than the speed of light. An umambiguous rewording of the phrase can now be made: The age of the Universe is defined as the largest possible value of proper time integrated along a timelike curve from the Earth at the present epoch back to the Big Bang. ...
The particle horizon in cosmology is the distance from which particles (of positive mass or of zero mass) can have travelled to the observer in the age of the Universe. ...
- For a "galaxy" towards or beyond the horizon, its "velocity", defined as comoving distance from the observer divided by the present cosmological time, can be greater than the speed of light.
This is a correct statement, but what is debatable is the philosophical interpretation. Problems according to a strictly empirical point of view (according to which something hidden inside a box does not exist, cf. Bertrand Russell) include: Empiricism (greek εμπειÏισμός, from empirical, latin experientia - the experience), is the philosophical doctrine that all human knowledge comes at first from senses and experience. ...
Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, OM (18 May 1872 – 2 February 1970) was an influential British mathematician, philosopher, and logician, working mostly in the 20th century. ...
- A distant "galaxy" towards the horizon is seen a long time in the past, when it was essentially just a lump of slightly overdense hydrogen with a bit of helium, so it is unlikely that stars had formed by then, so that the "galaxy" is impossible to observe.
- Moreover, a "galaxy" beyond the horizon can only be observed in the future.
- If you consider a distance to the "galaxy" defined by following the light path from that "galaxy", then this cannot be done for a "galaxy" beyond the horizon: the path does not arrive at the observer. On the other hand, for a "galaxy" inside the horizon, use of this same light-travel definition of distance, instead of comoving distance, can be done, but it yields a velocity less than the speed of light.
For these reasons, some people consider the comoving distance to be a merely theoretical construct with no physical meaning. However, in doing so, those people assert that the standard Big Bang model has no physical meaning, since comoving coordinates are an intrinsic part of the model. General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ...
General Name, Symbol, Number helium, He, 2 Chemical series noble gases Group, Period, Block 18, 1, s Appearance colorless Atomic mass 4. ...
According to the Big Bang theory, the universe originated in an extremely dense and hot state (bottom). ...
Other distances useful in cosmology - light-travel distance - simply the speed of light times the cosmological time interval, i.e. integral of (c dt), while the comoving distance is the integral of (c dt /a(t)).
- dL luminosity distance
- dpm proper motion distance
- (confusingly called the angular size distance by Peebles 1993 [2])
- sometimes called the coordinate distance
- sometimes dpm is called the angular diameter distance
- da angular diameter distance
The latter three are related by: - da = dpm / (1 + z) = dL /(1 + z)2
where z is the redshift.
If and only if the curvature is zero, then proper motion distance and comoving distance are identical, i.e. dpm = χ.
For negative curvature,
- ,
while for positive curvature, - ,
where RC is the (absolute value of the) radius of curvature. In mathematics, the absolute value (or modulus1) of a real number is its numerical value without regard to its sign. ...
A practical formula for numerically integrating dp to a redshift z for arbitrary values of the matter density parameter Ωm, the cosmological constant ΩΛ, and the quintessence parameter w is The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) occurs in Einsteins theory of general relativity. ...
The word Quintessence is used in different fields: In physics, Quintessence is a hypothetical form of energy postulated to exist as a possible explanation of observations of an accelerating universe. ...
where c is the speed of light and H0 is the Hubble constant. Cherenkov effect in a swimming pool nuclear reactor. ...
Hubbles law is the statement in astronomy that the redshift in light coming from distant galaxies is proportional to their distance. ...
By using sin and sinh functions, proper motion distance dpm can be obtained from dp.
Distances useful on small — galaxy or galaxy cluster — scales The ordinary distance as experienced by particles travelling slower than or at the speed of light is simply the comoving distance multiplied by the value of the scale factor at the cosmological time studied. The scale factor, parameter of Friedmann-Lemaître-Robertson-Walker model, is a function of time which represents the relative expansion of the universe. ...
Different names for this include
- physical distance - this has the problem that it suggests that comoving distance is less physical than ordinary distance.
- proper distance - this is confusing (see above) though correct if calculated at the cosmological time studied.
See also Friedmann-Lemaître-Robertson-Walker. The Friedmann-Lemaître-Robertson-Walker (FLRW) metric describes a homogeneous, isotropic expanding/contracting universe. ...
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