Dependence of density perturbations on the coupling constant in a simple model of inflation

In the standard inflationary scenario with inflaton potential V(Φ)=M⁴-1/4λΦ⁴, the resulting density perturbations δρρ are proportional to λ1/2. Upper bounds on δρρ require λ10^-13. Ratra has shown that an alternative treatment of reheating results in δρρ∝λ^-1, so that an upper bound on δρρ does not put an obvious upper bound on λ. We verify that δρρ∝λ^-1 is indeed a possibility, but show that λ10^-13 is still required.