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Density Parameter (Ω)

Represents the energy density of the universe relative to a critical density, influencing the fate of the universe according to inflationary models.
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The statement of the theorem

The density parameter Ω\Omega at any time tt is defined as the ratio of the total energy density ρ\rho to the critical density ρc(t)\rho_c(t): Ω(t)=ρ(t)ρc(t)=ρ(t)3H2/(8πG)\Omega(t) = \frac{\rho(t)}{\rho_c(t)} = \frac{\rho(t)}{3H^2/(8\pi G)} Assuming a perfect fluid description ρ(t)=∑iρi(t)\rho(t) = \sum_i \rho_i(t), the evolution of Ω\Omega is determined by the Friedmann equation: H2(t)=8πG3ρ(t)=8πG3∑iρi,0a(t)−3(1+wi)H^2(t) = \frac{8\pi G}{3} \rho(t) = \frac{8\pi G}{3} \sum_i \rho_{i,0} a(t)^{-3(1+w_i)} where wiw_i is the equation of state parameter for component ii.
Source: Wikipedia