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Integrating Friedmann Equation of Multicomponent universe respect to a and t 
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#1
Dec2812, 07:09 PM

P: 19

I am having a trouble finding relationship between 'a' and 't' by integrating friedmann equation in a multicomponent universe.
It would be very helpful if you can help me with just mattercurvature only universe and matterlambda only universe. The two integrals looks like following. Mattercurvature only: [tex]H_0 t = ∫_0^a \frac{da}{[Ω_0/a + (1Ω_0)]^{1/2}} [/tex] MatterLambda only: [tex]H_0 t = ∫_0^a \frac{da}{[Ω_0/a + (1Ω_0)a^2]^{1/2}} [/tex] Thank you for your help. 


#2
Dec2812, 10:01 PM

PF Gold
P: 184

Try substituting x = 1/a and then use a table of integrals.



#3
Dec3112, 12:25 AM

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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