Equation of state (cosmology)

Equation of state in 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 ε {\displaystyle \varepsilon } : w ≡ p ε . {\displaystyle w\equiv {\frac {p}{\varepsilon }}.} It is closely related to the thermodynamic equation of state and ideal gas law. The equation The perfect gas equation of state may be written as p = ρ R T = ρ c s 2 {\displaystyle p= ho RT= ho c_{s}^{2}} where ρ {\displaystyle ho } is the mass density, R {\displaystyle R} is the particular gas constant, T {\displaystyle T} is the temperature and c s = R T {\displaystyle c_{s}={\sqrt {RT}}} is a characteristic thermal speed of the molecules. Thus w ≡ p ρ c 2 = ρ c s 2 ρ c 2 = c s 2 c 2 ≈ 0 {\displaystyle w\equiv {\frac {p}{ ho c^{2}}}={\frac { ho c_{s}^{2}}{ ho c^{2}}}={\frac {c_{s}^{2}}{c^{2}}}\approx 0} where c {\displaystyle c} is the speed of light, ε = ρ c 2 {\displaystyle \varepsilon = ho c^{2}} and c s ≪ c {\displaystyle c_{s}\ll c} for a "cold" gas. FLRW equations and the equation of state The equation of state may be used in Friedmann–Lem