- #1

shinobi20

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##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.