Equation of state (cosmology)

In cosmology, the equation of state of a perfect fluid is characterized by a dimensionless number w {displaystyle w} , equal to the ratio of its pressure p {displaystyle p} to its energy density ρ {displaystyle ho }  : In cosmology, the equation of state of a perfect fluid is characterized by a dimensionless number w {displaystyle w} , equal to the ratio of its pressure p {displaystyle p} to its energy density ρ {displaystyle ho }  : It is closely related to the thermodynamic equation of state and ideal gas law. The perfect gas equation of state may be written as where ρ m {displaystyle ho _{m}} is the mass density, R {displaystyle R} is the particular gas constant, T {displaystyle T} is the temperature and C = R T {displaystyle C={sqrt {RT}}} is a characteristic thermal speed of the molecules. Thus where c {displaystyle c} is the speed of light, ρ = ρ m c 2 {displaystyle ho = ho _{m}c^{2}} and C ≪ c {displaystyle Cll c} for a 'cold' gas. The equation of state may be used in Friedmann–Lemaître–Robertson–Walker (FLRW) equations to describe the evolution of an isotropic universe filled with a perfect fluid. If a {displaystyle a} is the scale factor then If the fluid is the dominant form of matter in a flat universe, then where t {displaystyle t} is the proper time. In general the Friedmann acceleration equation is