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

Exponential potential for inflation

  1. Jan 8, 2014 #1
    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?
    Last edited: Jan 8, 2014
  2. jcsd
  3. Jan 9, 2014 #2


    User Avatar
    Science Advisor

    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


    User Avatar
    Science Advisor
    Gold Member

    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..
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook