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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


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    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].
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