Inflation in $F(R)$ gravity models revisited after ACT

TL;DR

This paper revisits $F(R)$ gravity models of inflation in light of recent ACT and DESI observations, proposing a new slow-roll description and a modified Starobinsky model that satisfy current cosmological constraints.

Contribution

It introduces a new slow-roll approximation in the Jordan frame and proposes a modified Starobinsky inflation model consistent with recent observational data.

Findings

ACT constraints significantly restrict $F(R)$ inflation models

Modified models can meet the scalar tilt $n_s$ and running $eta_s$ requirements

Proposes a unified $F(R)$ model with primordial black hole production

Abstract

The $F(R)$ gravity models of inflation are revisited in light of the recent observations of cosmic microwave background radiation by Atacama Cosmology Telescope (ACT) and DESI Collaboration. A detailed study of the evolution equations in the Jordan frame is given and a new description of the slow-roll approximation in the $F(R)$-gravity-based models of inflation is proposed. It is found that all those models of inflation are significantly constrained by demanding a higher (than the Planck Telescope value) cosmological tilt $n_s$ of scalar perturbations and a positive running index $\alpha_s$ favored by ACT. It is not difficult to meet the ACT constraints on the scalar tilt $n_s$ by modifying the existing models of inflation, but simultaneously demanding a positive running $\alpha_s$ would rule out many of them. Using the proposed slow-roll approximation in the Jordan frame, we provide a new modification of the Starobinsky inflation model in the framework of $F(R)$ gravity, which satisfies all ACT constraints. An extension of our ACT-consistent inflation model to the unified $F(R)$-gravity description of Starobinsky-like inflation and production of primordial black holes on a smaller scale is also proposed.