Physical cosmology

Age of the universe Big Bang Comoving distance Cosmic microwave background Dark energy Dark matter FLRW metric Friedmann equations Galaxy formation Hubble's law Inflation Large-scale structure Lambda-CDM model Metric expansion of space Nucleosynthesis Observable universe Redshift Shape of the universe Structure formation Timeline of the Big Bang Timeline of cosmology Ultimate fate of the universe Universe

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Astrophysics General relativity Particle physics Quantum gravity

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The Friedmann-Lemaître-Robertson-Walker (FLRW) metric is an exact solution of the Einstein field equations of general relativity and which describes a homogeneous, isotropic expanding/contracting universe. Depending on geographical/historical preferences, this may be referred to under the names of a preferred subset of the four scientists Alexander Friedmann, Georges Lemaître, Howard Percy Robertson and Arthur Geoffrey Walker, e.g. Friedmann-Robertson-Walker (FRW) or Robertson-Walker (RW). Cosmology, as a branch of astrophysics, is the study of the large-scale structure of the universe and is concerned with fundamental questions about its formation and evolution. ... Image File history File links Download high resolution version (2198x1274, 1278 KB)WMAP map of CMB anisotropy, from NASA.gov File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Nothing is certain as to the extent of either the age or size of the universe, but the age of the Universe, according to the Big Bang theory, is defined as the largest possible value of proper time integrated along a timelike curve from the Earth at the present epoch... According to the Big Bang theory, the universe emerged from an extremely dense and hot state (bottom). ... 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. ... In cosmology, the cosmic microwave background radiation (most often abbreviated CMB but occasionally CMBR, CBR or MBR) is a form of electromagnetic radiation discovered in 1965 that fills the entire universe. ... In physical cosmology, dark energy is a hypothetical form of energy which permeates all of space and has strong negative pressure. ... In astrophysics, dark matter refers to matter that does not emit or reflect enough electromagnetic radiation (such as light, x-rays and so on) to be detected directly, but whose presence may be inferred from its gravitational effects on visible matter. ... 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. ... REDIRECT [[ --68. ... 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. ... A pie chart indicating the proportional composition of different energy-density components of the universe. ... The metric expansion of space is a key part of sciences current understanding of the universe, whereby space itself is described by a metric which changes over time. ... In cosmology, Big Bang nucleosynthesis (or primordial nucleosynthesis) refers to the production of nuclei other than H-1, the normal, light hydrogen, during the early phases of the universe, shortly after the Big Bang. ... The observable Universe is a term used in cosmology to describe a ball-shaped region of space surrounding the Earth that is close enough that we might observe objects in it. ... Redshift of spectral lines in the optical spectrum of a supercluster of distant galaxies (right), as compared to that of the Sun (left). ... The shape of the Universe is a subject of investigation within cosmology. ... It has been suggested that this article or section be merged into Large-scale structure of the cosmos. ... A graphical timeline is available here: Graphical timeline of the Big Bang This timeline of the Big Bang describes the events that have occurred and will occur according to the scientific theory of the Big Bang. ... The timeline of cosmology lists the sequence of cosmological theories and discoveries in chronological order. ... The ultimate fate of our universe is a topic in physical cosmology. ... The deepest visible-light image of the cosmos, the Hubble Ultra Deep Field. ... 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 celestial objects such as stars, galaxies, and the interstellar medium, as well as their interactions. ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... Particles explode from the collision point of two relativistic (100 GeV per nucleon) 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. ... In mathematics, in Riemannian geometry, the metric tensor is a tensor of rank 2 that is used to measure distance and angle in a space. ... Category: Mathematics stubs ... This article or section is in need of attention from an expert on the subject. ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ... The metric expansion of space is a key part of sciences current understanding of the universe, whereby space itself is described by a metric which changes over time. ... The deepest visible-light image of the cosmos, the Hubble Ultra Deep Field. ... Alexander Alexandrovich Friedman (June 16, 1888 – September 16, Russian cosmologist and mathematician. ... Father Georges-Henri Lemaître (July 17, 1894 – June 20, 1966) was a Belgian Roman Catholic priest, honorary prelate, professor of physics and a astronomer. ... Howard Percy Robertson (January 27, 1903 - August 26, 1961) was a scientist known for contributions related to cosmology and the uncertainty principle. ... Arthur Geoffrey Walker (17 July 1909 - 31 March 2001) was a leading mathematician and cosmologist. ...

The FLRW metric is used as a first approximation for the standard big bang cosmological model of the universe. Because the FLRW assumes homogeneity, some popular accounts mistakenly assert that the big bang model cannot account for the observed lumpiness of the universe. In actuality, the FLRW is used as a first approximation for the evolution of the universe because it is simple to calculate, and models which calculate the lumpiness in the universe are added onto FLRW as extensions. As of 2003, the theoretical implications of the various extensions to FLRW appear to be well understood, and the goal is to make these consistent with observations from COBE and WMAP. According to the Big Bang theory, the universe emerged from an extremely dense and hot state (bottom). ... 2003 is a common year starting on Wednesday of the Gregorian calendar, and also: The International Year of Freshwater The European Disability Year Events January events January 1 Luíz Inácio Lula Da Silva becomes the 37th President of Brazil. ... The Cosmic Background Explorer (COBE), also referred to as Explorer 66, was the first satellite built dedicated to cosmology. ... Artist depiction of the WMAP satellite at the L2 point The Wilkinson Microwave Anisotropy Probe (WMAP) is a NASA satellite whose mission is to survey the sky to measure the temperature of the radiant heat left over from the Big Bang. ...

The metric can be written as

where:

a(t) = the scale factor of the universe at time t

where R_C = the absolute value of the radius of curvature

dΩ² = dθ² + sin²θdφ²

In this formulation of the metric,

r gives the comoving distance from the observer

gives the proper motion distance.

Under the assumptions of homogeneity and isotropy, together with an appropriate energy-momentum tensor, the Einstein field equations reduce to the Friedmann equations. The solution of the Friedmann equations is the FLRW metric. Most cosmologists agree that the observable universe is well approximated by an almost FLRW model, that is, a model which follows the FLRW metric apart from primordial density fluctuations. In a strictly FLRW model, there are no clusters of galaxies, stars or people, since these are objects much denser than a typical part of the universe. The scale factor, parameter of Friedmann-Lemaître-Robertson-Walker model, is a function of time which represents the relative expansion of the universe. ... In mathematics, the absolute value (or modulus1) of a real number is its numerical value without regard to its sign. ... 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. ... In physics, proper length is the length of an object or a contour as measured in the reference frame of the object itself in the context of special relativity. ... The stress tensor or energy-momentum tensor is the corresponding conserved Noether current of any theory which is invariant under spacetime translations. ... This article or section is in need of attention from an expert on the subject. ... The Friedmann equations relate various cosmological parameters within the context of general relativity. ... The observable Universe is a term used in cosmology to describe a ball-shaped region of space surrounding the Earth that is close enough that we might observe objects in it. ... Primordial fluctuations are density variations in the early universe which are considered the seeds of all structure in the universe. ...

However, for brevity, the almost FLRW model is often referred to simply as the FLRW model (or the FRW model).

External links

• Ellis, George F. R., van Elst, Henk. Cosmological models (Cargèse lectures 1998). arXiv.org eprint archive. Retrieved on July 30, 2005.

July 30 is the 211th day (212th in leap years) of the year in the Gregorian Calendar, with 154 days remaining. ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ...

References

• d'Inverno, Ray (1992). Introducing Einstein's Relativity. Oxford: Oxford University Press. ISBN 0-19-859686-3.. See chapter 23 for a particularly clear and concise introduction to the FLRW models.