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Density Parameter

Ω = ρ/ (ρc) represents the density parameter, where ρ is the energy density and ρc is the critical density, crucial for determining the universe's fate.
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The statement of the theorem

The density parameter Ω\Omega quantifies the ratio of the actual energy density ρ\rho to the critical density ρc\rho_c. It is defined as: \nΩ=ρρc\Omega = \frac{\rho}{\rho_c}The critical density ρc\rho_c is derived from the Friedmann equation at t=t0t=t_0 and is given by:\nρc=3H028πG\rho_c = \frac{3H_0^2}{8\pi G}The total density parameter Ωtotal\Omega_{total} determines the geometry of the universe: Ωtotal=1\Omega_{total} = 1 implies a flat (Euclidean) geometry, Ωtotal>1\Omega_{total} > 1 implies a closed (spherical) geometry, and Ωtotal<1\Omega_{total} < 1 implies an open (hyperbolic) geometry.
Source: Wikipedia