Tabletop potentials for inflation from f(R) gravity

Abstract We show that a large class of modified gravity theories (MOG) with the Jordan-frame Lagrangian f ( R ) translate into scalar-field (scalaron) models with hilltop potentials in the Einstein frame. (A rare exception to this rule is provided by the Starobinsky model for which the corresponding scalaron potential is plateau-like for ϕ > 0.) We find that MOG models featuring two distinct mass scales lead to scalaron potentials that have a flattened hilltop, or tabletop . Inflationary evolution in tabletop models agrees very well with CMB observations. Tabletop potentials therefore provide a new and compelling class of MOG-based inflationary models. By contrast, MOG models with a single mass scale generally correspond to steep hilltop potentials and fail to reproduce the CMB power spectrum. Inflationary evolution in hilltop/tabletop models can proceed in two alternative directions: towards the stable point at small R describing the observable universe, or towards the asymptotic region at large R . The MOG models which we examine have several new properties including the fact that gravity can become asymptotically vanishing, with G eff → 0, at infinite or large finite values of the scalar curvature R . A universe evolving towards the asymptotically vanishing gravity region at large R will either run into a 'Big-Rip' singularity, or inflate eternally.