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

  1. Mar 30, 2010 #1
    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).....(*)


    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!

  2. jcsd
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