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

Abstract

In the standard inflationary scenario with inflaton potential $V(Φ)=M^4-{1\over4}λΦ^4$, the resulting density perturbations $δρ/ρ$ are proportional to $λ^{1/2}$. Upper bounds on $δρ/ρ$ require $λ< 10^{-13}$. Ratra has shown that an alternative treatment of reheating results in $δρ/ρ\propto λ^{-1}$, so that an upper bound on $δρ/ρ$ does not put an obvious upper bound on $λ$. We verify that $δρ/ρ\propto λ^{-1}$ is indeed a possibility, but show that $λ< 10^{-13}$ is still required.