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Exponential potential for inflation

  1. Jan 8, 2014 #1
    hi
    I want to solve inflation problem for exponential potential.
    [tex] v(\phi) = v_0 exp(-\alpha \phi) [/tex]
    (it's known as barrow or pawer law inflation )
    we have 2 main equations:
    [tex] H^2 = 8π G / 3 (1/2 (\dot{\phi})^2 + v(\phi)) [/tex]
    [tex] \ddot{\phi} + 3H \dot{\phi} + v(\phi)'=0 [/tex]
    I must solve this 2 equ and find [itex] \phi(t) [/itex] and H(Hubble).
    in the book of cosmology by weinberg has written,it is easy but i can't do it.can anyone help me?
    best
     
    Last edited: Jan 8, 2014
  2. jcsd
  3. Jan 9, 2014 #2

    Chalnoth

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    The assumption of slow-roll inflation is that [itex]\ddot{\phi}[/itex] is small compared to the "friction" term [itex]3H\dot{\phi}[/itex], and thus can be neglected.

    So your job is basically two-fold:
    1. Solve the equations in the slow-roll regime.
    2. Show the parameter values for which the slow-roll regime is valid.
     
  4. Jan 9, 2014 #3

    Chronos

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    You made this problem way too easy to solve, Chalnoth.
     
  5. Jan 12, 2014 #4
    thanks,but I think that it has exact solution.without slow-roll condition..
     
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