# Homework Help: Calculating the Redshift at which the Universe was dominated by different components

1. Mar 30, 2010

1. The problem statement, all variables and given/known data

Hey :-)

I want to calculate the redshift at which the Universe became vacuum dominated, with given values for the energy densities of Omega_{m} and Omega_{Lambda}.

2. Relevant equations

I know that the scale factors

rho_{m} is proportional to a^{-3}
rho_{r} is proportional to a^{-4}
rho_{v} is proportional to a^{0}

I know that the relationship between the scale factor and the redshift is

(1+z) = a(t) / a_{0}(t).....(*)

and

H^{2} = h_{0}^2 [ Omega_{m}/a^{3} + Omega_{r}/a^{4} + Omega_{Lambda} + Omega_{k}/a^{2} ]

3. The attempt at a solution

I know that at early enough times the Universe was radiation dominated. I have plotted log rho vs log a for each contributor, and can see that the Universe was originally radiation dominated, then matter dominated, then vacuum dominated. I thought that if I calculated the point at which the matter and vacuum slopes intersected, I could solve for a, and then use equation (*), but I wouldn't know what to use for a_{0}. And if I did equate a^{-3} to a^{0}, I just get 1. And that wouldn't be using the given values for Omega_{Lambda} or Omega_{m}.

I'm not very confident in my approach and any advice would be warmly appreciated!

Thanks