Calculations of inflaton decays and reheating: with applications to no-scale inflation models

We discuss inflaton decays and reheating in no-scale Starobinsky-like models of inflation, calculating the effective equation-of-state parameter, w, during the epoch of inflaton decay, the reheating temperature, T{sub reh}, and the number of inflationary e-folds, N{sub ∗}, comparing analytical approximations with numerical calculations. We then illustrate these results with applications to models based on no-scale supergravity and motivated by generic string compactifications, including scenarios where the inflaton is identified as an untwisted-sector matter field with direct Yukawa couplings to MSSM fields, and where the inflaton decays via gravitational-strength interactions. Finally, we use our results to discuss the constraints on these models imposed by present measurements of the scalar spectral index n{sub s} and the tensor-to-scalar perturbation ratio r, converting them into constraints on N{sub ∗}, the inflaton decay rate and other parameters of specific no-scale inflationary models.