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 $\varphi >0$.) 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 $G_{\mathrm{eff}}\to 0$, 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.

35 pages, 11 figures, revised version, some clarifications and additional references, matches published version in JCAP

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Cited by in corpus (10)

• Cornering Extended Starobinsky Inflation with CMB and SKA
• Spherically symmetric configurations in the quadratic $f(R)$ gravity
• Stability investigations of isotropic and anisotropic exponential inflation in the Starobinsky-Bel-Robinson gravity
• Inflation in Weyl Scaling Invariant Gravity with $R^3$ Extensions
• Purely gravitational dark matter production in warm inflation
• Interactions of the scalaron dark matter in $f(R)$ gravity
• Stability investigations of de Sitter inflationary solutions in power-law extensions of the Starobinsky model
• Inflation in light of ACT/SPT: A new perspective from Weyl gravity
• Effective scalaron--photon interaction in $f(R)$ gravity
• Universality in static spherically symmetric solutions of f(R) gravity