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F(R) gravity and the Hubble parameter

  1. Feb 12, 2016 #1
    Dear all,

    Considering Einstein Hilbert lagrangian, by using Einstein field equations one can get the form of Friedman equations and consequently the Hubble parameter.
    I know that in f(R) models, Einstein equations get modified. However, what happens to the Friedman equation and the Hubble parameter?
    I tried to solve them and get to the form of H, but it seems such a complicated equation.

    Using the (00) component, I get
    \begin{equation}
    H^2=\frac{8\pi G}{3}\rho -\frac{6\alpha}{c^2}(\frac{\ddot{a}^2}{a^2} + H^4)
    \end{equation}
    What should I do with the
    \begin{equation} \ddot{a}^2\end{equation}
    in the first equation?!!
    The (11) component just makes everything more complicated!!
    I really appreciate any help or idea.
    BTW, I am using FRW metric.
     
    Last edited: Feb 12, 2016
  2. jcsd
  3. Feb 12, 2016 #2
    I just realized that the equations consist the forth order of the scale factor (a(t)).
    Are these solvable in the matter dominated era? when
    \begin{equation}
    \rho(z)=\rho_m a^{-3}
    \end{equation}
     
  4. Feb 15, 2016 #3
    Has anybody seen any paper on the change of hubble parameter with f(R)? Is there at least any approximation?
     
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