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The first Friedmann equation is often seen in terms of the present values of the density parameters, that is [7] =, +, +, +,. Here Ω 0,R is the radiation density today (when a = 1 ), Ω 0,M is the matter ( dark plus baryonic ) density today, Ω 0, k = 1 − Ω 0 is the "spatial curvature density" today, and Ω 0,Λ is the cosmological constant ...
The first equation can be derived also from thermodynamical considerations and is equivalent to the first law of thermodynamics, assuming the expansion of the universe is an adiabatic process (which is implicitly assumed in the derivation of the Friedmann–Lemaître–Robertson–Walker metric).
The Einstein–de Sitter universe is a model of the universe proposed by Albert Einstein and Willem de Sitter in 1932. [1] On first learning of Edwin Hubble's discovery of a linear relation between the redshift of the galaxies and their distance, [2] Einstein set the cosmological constant to zero in the Friedmann equations, resulting in a model of the expanding universe known as the Friedmann ...
The Milne universe is a special case of a more general Friedmann–Lemaître–Robertson–Walker model (FLRW). The Milne solution can be obtained from the more generic FLRW model by demanding that the energy density, pressure and cosmological constant all equal zero and the spatial curvature is negative.
This combination greatly simplifies the equations of general relativity into a form called the Friedmann equations. These equations specify the evolution of the scale factor the universe in terms of the pressure and density of a perfect fluid. The evolving density is composed of different kinds of energy and matter, each with its own role in ...
Also known as the cosmic scale factor or sometimes the Robertson–Walker scale factor, [1] this is a key parameter of the Friedmann equations. In the early stages of the Big Bang , most of the energy was in the form of radiation, and that radiation was the dominant influence on the expansion of the universe.
The Friedmann acceleration equation can be written as ¨ = (+) = (+), where the sum extends over the different components, matter, radiation and dark energy, is the equivalent mass density of each component, is its pressure, and = / is the equation of state for each component.
The cosmological constant was originally introduced in Einstein's 1917 paper entitled “The cosmological considerations in the General Theory of Reality”. [2] Einstein included the cosmological constant as a term in his field equations for general relativity because he was dissatisfied that otherwise his equations did not allow for a static universe: gravity would cause a universe that was ...