Constant-roll $f(R)$ inflation compared with Cosmic Microwave Background anisotropies and swampland criteria

Abstract

Inflationary models derived from f (R) gravity, where the scalaron rolls down with a constant rate from the top to the minimum of the effective potential, are considered. Specifically, we take into account three f (R) models i.e. Starobinsky R 2 , R 2p and the logarithmic corrected models. We compare the inflationary parameters derived from the models with the observational data of CMB anisotropies i.e. the Planck and Keck/array datasets in order to find observational constraints on the parameters space. We find that although our f (R) constant-roll models for γ = 0 show observationally acceptable values of r, they do not predict favoured values of the spectral index.In particular, we have ns > 1 for the Starobinsky R 2 and R 2p models and 0.996 < ns < 0.999 for logarithmic model. Finally, we study the models from the point of view of Weak Gravity Conjecture adopting the swampland criteria.