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.

arXiv comment35 pages, 11 figures, revised version, some clarifications and additional references, matches published version in JCAP

References in corpus (33)

• f(R) Theories Of Gravity
• f(R) theories
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Planck 2018 results. X. Constraints on inflation
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Do consistent $F(R)$ models mimic General Relativity plus $\Lambda$?
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Constraining f(R) Gravity as a Scalar Tensor Theory
• Cosmological dynamics of R^n gravity
• Dark energy and dark matter as curvature effects
• Dark Matter from R^2-gravity
• Occurrence of exact $R^2$ inflation in non-local UV-complete gravity
• A polynomial f(R) inflation model
• Dark energy, inflation and dark matter from modified F(R) gravity
• Dynamical and Gravitational Instability of Oscillating-Field Dark Energy and Dark Matter
• Viable Singularity-Free f(R) Gravity Without a Cosmological Constant
• Modified Gravity Explains Dark Matter?
• Inflation in the closed FLRW model and the CMB
• Cosmic History of Chameleonic Dark Matter in $F(R)$ Gravity
• Dark matter as scalaron in $f(R)$ gravity models
• Scalarons mimicking Dark Matter in the Hu-Sawicki model of f(R) gravity
• Higher-order extension of Starobinsky inflation: initial conditions, slow-roll regime, and reheating phase
• High-energy scalarons in R^{2} gravity as a model for Dark Matter in galaxies
• Light scalaron as dark matter
• Stable super-inflating cosmological solutions in f(R)-gravity
• Are $R^2$- and Higgs-inflations really unlikely?
• Tensor perturbations during inflation in a spatially closed Universe
• Generalized non-local $R^2$-like inflation
• Unified $f(R)$ gravity at local scales
• Initial conditions for the scalaron dark matter
• On the Conformal Frames in $f(R)$ Gravity
• Asymptotic solutions in f(R)-gravity

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