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

I Nonlinear integration

  1. Feb 9, 2017 #1
    From cosmology, the friedmann equations are given by,
    ##H^2 = (\frac{\dot a}{a})^2 = \frac{8\pi G}{3} \rho \, , \quad \frac{\ddot a}{a} = -\frac{4\pi G}{3}(\rho+3p) \, , \quad## where ##\rho = \frac{1}{2}(\dot \phi^2 + \phi^2)## and ##p = \frac{1}{2}(\dot \phi^2 - \phi^2)##

    To get ##\dot H##,
    ##\dot H = \frac{d}{dt}(\frac{\dot a}{a}) = \frac{\ddot a}{a} - (\frac{\dot a}{a})^2 = -4\pi G(\rho + p) = -4\pi G \dot \phi^2##.

    I want to solve for ##H## using this equation, where ##0<t<10^7##. How should I solve this DE? It's ok if the solution is in the implicit form.
     
  2. jcsd
  3. Feb 16, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
  4. Feb 16, 2017 #3
    Hi shinobi:

    When solving for H(t) I would generally work with a different form of the Friedmann equation.
    The one I mean is in the article just above "Useful Solutions".

    H is given as a function of a, together with the parameter H0, and several density ratio parameters, the Ωs with various subscripts.
    Since H = (1/a) (da/dt), dt can be expressed in the form f(a) da. This can be numerically integrated to get t(a) for a specific value of a. I found the following online tool useful for this.
    You many want to substitute a = e-x if you find problems with the tool when integrating the f(a) form.

    I hope this is helpful.

    Regards,
    Buzz
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Nonlinear integration
  1. Nonlinear ODE (Replies: 2)

  2. Nonlinear Elasticity (Replies: 1)

  3. Nonlinear nightmare (Replies: 7)

Loading...