Friedmann Equation Density Parameter. The curvature parameter indicates whether the universe is open or closed. The criticaldensity and the density parameter ω substituting h t a a allows us to write the friedmann equation in terms of the hubble param eter h2 t 8πg 3 ǫ t c2 kc2 r2 0 1 a2 t.
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The variable k is the curvature parameter of the universe and can be either 1 0 or 1 for a closed flat and open universe respectively. In this equation g is the gravitational constant 6 67 10 11nm2 kg2 ρris the radiation density of the universe ρmis the matter density of the universe and ρdis the dark energy density of the universe. ρm ρm 0 a0 a 3 ρm ρm 0a 3.
For a matter dominated universe the density varies as.
Besides the density and gravitation constant g the equation contains the hubble parameter h a scaling parameter r and a factor k which is called the curvature parameter. The variable k is the curvature parameter of the universe and can be either 1 0 or 1 for a closed flat and open universe respectively. The density parameter ω ultimately governs whether the curvature is. Negative ω 1 positive ω 1 flat ω 1 rewriting the friedmann equation in integral form.
