# Integrating Friedmann Equation of Multi-component universe respect to a and t

by 4everphysics
Tags: equation, friedmann, integrating, multicomponent, respect, universe
 P: 19 I am having a trouble finding relationship between 'a' and 't' by integrating friedmann equation in a multi-component universe. It would be very helpful if you can help me with just matter-curvature only universe and matter-lambda only universe. The two integrals looks like following. Matter-curvature only: $$H_0 t = ∫_0^a \frac{da}{[Ω_0/a + (1-Ω_0)]^{1/2}}$$ Matter-Lambda only: $$H_0 t = ∫_0^a \frac{da}{[Ω_0/a + (1-Ω_0)a^2]^{1/2}}$$ Thank you for your help.
 PF Gold P: 184 Try substituting x = 1/a and then use a table of integrals.
 P: 2 with matter lambda the result is a(t)=(ro_matter/ro_lambda)^(1/3)*[sinh[(6*Pi*ro_lambda*G)^(1/2)*t]^(2/3) Where ro_x/ro_critical=omega_0x

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