Register to reply

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

Share this thread:
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.
Phys.Org News Partner Space news on
Chilly end for sex geckos sent into space by Russia
Memory reformat planned for Opportunity Mars rover
Magnetar discovered close to supernova remnant Kesteven 79
Dec28-12, 10:01 PM
PF Gold
P: 184
Try substituting x = 1/a and then use a table of integrals.
Dec31-12, 12:25 AM
P: 2
with matter lambda the result is
Where ro_x/ro_critical=omega_0x

Register to reply

Related Discussions
Integrating the Complex conjugate of z with respect to z Calculus & Beyond Homework 5
Finding centroids when integrating with respect to y Calculus & Beyond Homework 1
The Friedmann equation in a lambda-dominated universe Advanced Physics Homework 4
Why do we live in a Friedmann universe? Cosmology 10
Friedmann Equation and the age of empty universe Advanced Physics Homework 2