Dependence of Density Perturbations on the Coupling Constant in a Simple Model of Inflation

Abstract

In the standard inflationary scenario with inflaton potential $V(\Phi )=M^4-\frac{1}{4}\lambda {\Phi }^4$, the resulting density perturbations $\delta \rho /\rho$ are proportional to ${\lambda }^{1/2}$. Upper bounds on $\delta \rho /\rho$ require $\lambda <10^{-13}$. Ratra has shown that an alternative treatment of reheating results in $\delta \rho /\rho \propto {\lambda }^{-1}$, so that an upper bound on $\delta \rho /\rho$ does not put an obvious upper bound on $\lambda$. We verify that $\delta \rho /\rho \propto {\lambda }^{-1}$ is indeed a possibility, but show that $\lambda <10^{-13}$ is still required.

6 pages, in Plain Tex, UCSBTH-92-20

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