Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Conformal time analytical expression

  1. Aug 5, 2010 #1
    Hi all,
    Anybody pls help me to convert cosmic time to conformal time (numerically)...
    is there any analytical expression for conformal time, \tau , except d\tau=dt/a(t) ?
    can we approximate \tau \approx -1/aH ??

    pls help...

  2. jcsd
  3. Aug 5, 2010 #2


    User Avatar
    Science Advisor

    You can obtain an analytic expression for \tau whenever you know the time dependence of the scale factor, a(t). During de Sitter expansion, one has

    [tex]a(t) \propto e^{Ht}[/tex]

    giving a conformal time of [tex]\tau = 1/aH [/tex]. So that approximation you give is only good for near de Sitter expansion, when the rate of change of the Hubble parameter is small:

    [tex]\frac{\dot{H}}{H^2} \ll 1[/tex].
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook