1
$\begingroup$

Assume that $\phi=\phi_0\gg M_{Pl}$, what can you say about the future of a universe in a model with $V(\phi)=\frac{1}{2}m^2\phi^2+\epsilon \phi$, where $|\epsilon|\ll m^2M_{Pl}^2$, is a small parameter and $m$ is such that $V(\phi_0)\approx \rho_c$.

My method is: I used Klein Gordon Equation \begin{equation}\ddot{\phi}+3H\dot{\phi}+V'=0,\end{equation}

where $V'=m^2\phi+\epsilon$. After this I can solve for $\phi$ by using the slow roll conditions. But, what am I supposed to do afterwards? What does the future of universe mean? Am I supposed to show whether the universe will expand or contract?

$\endgroup$
4
  • $\begingroup$ If $\Phi$ and $m$ have mass dimension $1$, $\epsilon$ must have mass dimension $3$ , not $4$ $\endgroup$
    – Trimok
    Commented Jul 15, 2014 at 9:07
  • $\begingroup$ IHMO, you have to use the Einstein equations, see for instance equations $(7), (8)$, and the discussion in chapters $3 \to 8$ in this paper $\endgroup$
    – Trimok
    Commented Jul 15, 2014 at 9:26
  • $\begingroup$ But $\epsilon$ has mass dimension of 3, I guess, because $M_{pl}^2$ has mass dimension of 1. $\endgroup$
    – titanium
    Commented Jul 16, 2014 at 0:53
  • $\begingroup$ No, $M_{pl}$ has mass dimension $1$, so $M_{pl}^2$ has mass dimensions $2$. Otherwise, give the precise mass dimension of $\Phi,m, M_{pl}..$ $\endgroup$
    – Trimok
    Commented Jul 16, 2014 at 8:11

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.