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

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4everphysics
#1
Dec28-12, 07:09 PM
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:

[tex]H_0 t = ∫_0^a \frac{da}{[Ω_0/a + (1-Ω_0)]^{1/2}} [/tex]

Matter-Lambda only:

[tex]H_0 t = ∫_0^a \frac{da}{[Ω_0/a + (1-Ω_0)a^2]^{1/2}} [/tex]

Thank you for your help.
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BillSaltLake
#2
Dec28-12, 10:01 PM
PF Gold
P: 184
Try substituting x = 1/a and then use a table of integrals.
akhtarphysic
#3
Dec31-12, 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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