NationMaster - Encyclopedia: Friedmann equations

edit 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. ... 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). ... 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. ... In cosmology, dark energy is a hypothetical form of energy which permeates all of space and has strong negative pressure. ... This refers to the cosmological use of the term. ... The Friedmann-LemaÃ®tre-Robertson-Walker (FLRW) metric describes a homogeneous, isotropic expanding/contracting universe. ... 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. ... Î›CDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter. ... In cosmology, Big Bang nucleosynthesis (alternately: 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. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... The timeline of cosmology lists the sequence of cosmological theories and discoveries in chronological order. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... The deepest visible-light image of the cosmos. ... Spiral Galaxy ESO 269-57 Astrophysics is the tree 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. ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... Particles erupt from the collision point of two relativistic (100GeV) 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 Friedmann equations relate various cosmological parameters within the context of general relativity. They were derived by Alexander Friedmann in 1922 from the Einstein field equations under some assumptions of symmetry appropriate for a cosmological model. From his equations, the Friedmann-Lemaître-Robertson-Walker metric was derived for a fluid with a given density and pressure. The equations are: Cosmology, from the Greek: κοσμολογία (cosmologia, κόσμος (cosmos) world + λογια (logia) discourse) is the study of the universe in its totality and by extension mans place in it. ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... Alexander Alexandrovich Friedman or Friedmann (ÐÐ»ÐµÐºÑÐ°Ð½Ð´Ñ€ ÐÐ»ÐµÐºÑÐ°Ð½Ð´Ñ€Ð¾Ð²Ð¸Ñ‡ Ð¤Ñ€Ð¸Ð´Ð¼Ð°Ð½) (June 16, 1888 â€“ September 16, 1925) was a Russian cosmologist and mathematician. ... 1922 (MCMXXII) was a common year starting on Sunday (see link for calendar). ... For other topics related to Einstein see Einstein (disambig) In physics, the Einstein field equation or the Einstein equation is a tensor equation in the theory of gravitation. ... 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. ... The Friedmann-LemaÃ®tre-Robertson-Walker (FLRW) metric describes a homogeneous, isotropic expanding/contracting universe. ... Density (symbol: Ï - Greek: rho) is a measure of mass per unit of volume. ... Pressure (symbol: p) is the force per unit area acting on a surface in a direction perpendicular to that surface. ...

$H^2 = left(frac{dot{a}}{a}right)^2 = frac{8 pi G}{3}rho + frac{Lambda}{3} - frac{k}{a^2}$

$frac{ddot{a}}{a} = -frac{4 pi G}{3}left(rho + 3pright) + frac{Lambda}{3}$

where $ρ$ and $p$ are the density and pressure of the fluid, $Λ$ is the cosmological constant possibly caused by vacuum energy, $G$ is the gravitational constant, $k$ gives the shape of the universe, and $a$ is the scale factor. The Hubble parameter $H$ is the rate of expansion of the universe, a value that can change over time if other parts of the equation are time dependent (in particular the energy density, vacuum energy, and curvature). Evaluating the Hubble parameter at the present time yields the Hubble constant which is the proportionality constant of Hubble's Law. Applied to a fluid with a given equation of state, the Friedmann equations yield the time evolution and geometry of the universe as a function of the fluid density. The cosmological constant (usually denoted by the Greek capital letter lambda: Î›) occurs in Einsteins theory of general relativity. ... Vacuum energy is an underlying background energy that exists in space even when devoid of matter. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... The shape of the Universe is a subject of investigation within cosmology. ... The scale factor, parameter of Friedmann-Lemaître-Robertson-Walker model, is a function of time which represents the relative expansion of the universe. ... Hubbles law is the statement in astronomy that the redshift in light coming from distant galaxies is proportional to their distance. ... A watch Attempting to understand time has long been a prime occupation for philosophers, scientists and artists. ... Hubbles law is the statement in physical cosmology that the redshift in light coming from distant galaxies is proportional to their distance. ... In physics and thermodynamics, an equation of state is a constitutive equation describing the state of matter under a given set of physical conditions. ...

Some cosmologists call the second of these two equations the acceleration equation and reserve the term Friedmann equation for only the first equation.

The density parameter

The first of the Friedmann equations defines a density parameter useful for comparing different cosmological models:

$Omega equiv frac{rho}{rho_c} = frac{8 pi G}{3 H^2}rho$

This term originally was used as a means to determine the geometry of the field where $ρ c$ is the critical density for which the geometry is flat. Assuming a zero vacuum energy density, if $Ω$ is larger than unity, the geometry is closed. If $Ω$ is less than unity, it is open. However, one can also subsume the curvature and vacuum energy terms into a more general expression for $Ω$ in which case this energy density parameter equals exactly unity. Then it is a matter of measuring the different components, usually designated by subscripts. According to the Lambda-CDM model, there are important components of $Ω$ due to baryons, cold dark matter and dark energy. The geometry of spacetime has been measured by the WMAP probe to be nearly flat meaning that the curvature parameter κ is zero. The shape of the Universe is a subject of investigation within cosmology. ... Î›CDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter. ... In particle physics, the baryons are a family of subatomic particles including the proton and the neutron (collectively called Greek barys, meaning heavy, as they are heavier than the other main groups of particles. ... Cold dark matter (or CDM) is a refinement of the big bang theory that contains the additional assumption that most of the matter in the Universe consists of material which cannot be observed by its electromagnetic radiation and hence is dark while at the same time the particles making up... In cosmology, dark energy is a hypothetical form of energy which permeates all of space and has strong negative pressure. ... World line of the orbit of the Earth depicted in two spatial dimensions X and Y (the plane of the Earth orbit) and a time dimension, usually put as the vertical axis. ... Alternate meaning: WMAP (AM) 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. ...

rescaled Friedmann equation

Set a=ãa₀, ρ_c=3H₀²/8π, ρ=ρ_cΩ, $t=tilde{t}/H_0$ , Ω_c=-κ/H₀²a₀² where a₀ and H₀ are seperately the scale factor and the Hubble parameter today. Then we can have The scale factor, parameter of Friedmann-Lemaître-Robertson-Walker model, is a function of time which represents the relative expansion of the universe. ... Hubbles law is the statement in astronomy that the redshift in light coming from distant galaxies is proportional to their distance. ...

$frac{1}{2}left( frac{dtilde{a}}{dtilde{t}}right)^2 + U_{eff}(tilde{a})=frac{1}{2}Omega_c$

where U_eff(ã)=Ωã²/2. For any form of the effective potential U_eff(ã), there is an equaiton of state p=p(ρ) that will produce it.

Categories: Cosmology | General relativity | Equations | Relativity stubs

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Friedmann equations - Wikipedia, the free encyclopedia (443 words)
	They were derived by Alexander Friedmann in 1922 from the Einstein field equations under some assumptions of symmetry appropriate for a cosmological model.
	From his equations, the Friedmann-Lemaître-Robertson-Walker metric was derived for a fluid with a given density and pressure.
	Applied to a fluid with a given equation of state, the Friedmann equations yield the time evolution and geometry of the universe as a function of the fluid density.

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rescaled Friedmann equation

The density parameter