  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, $T_{\rm reh}$,
and the number of inflationary e-folds, $N_*$, 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 $n_s$ and
the tensor-to-scalar perturbation ratio $r$, converting them into constraints
on $N_*$, the inflaton decay rate and other parameters of specific no-scale
inflationary models.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Theory