Effects of radiative corrections on Starobinsky inflation

We analyze radiative corrections to the predictions of Starobinsky-like models of inflation arising from self-interactions of the inflaton, and from its Yukawa couplings, y, to matter fermions, and dimensionful trilinear couplings, κ, to scalar fields, which could be responsible for reheating the Universe after inflation. The inflaton self-interactions are found to be of higher order in the Hubble expansion rate during inflation, and hence unimportant for CMB observations. In contrast, Einstein-frame matter couplings to an inflaton generating Starobinsky-like inflation can have significant effects on the spectral index of scalar CMB perturbations, n_s, and on the tensor-to-scalar ratio, r. Using a renormalization-group improved analysis of the effective inflationary potential, we find that the Planck measurement of n_s constrains the inflaton coupling to light fermions in the Einstein frame; y < 4.5 × 10⁻⁴, corresponding to an upper limit on the reheating temperature T_RH < 2 × 10¹¹ GeV, whereas the ACT DR6 measurement of n_s corresponds to 3.8 × 10⁻⁴ < y < 5.6 × 10⁻⁴ and 1.7 × 10¹¹ GeV < T_RH < 2.8 × 10¹¹ GeV, while the upper limits on r provide weaker constraints. Planck data also imply a constraint on a trilinear inflaton coupling to light scalars in the Einstein frame: κ ≤ 4 × 10¹² GeV, corresponding to T_RH ≤ 4.2 × 10¹³ GeV. We further present constraints on inflaton couplings to massive fermions and scalars, and analyze constraints on couplings in the Jordan frame.