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

TL;DR

The paper addresses tensions between Planck and ACT/DESI constraints on inflation, proposing a slow-roll framework formulated directly in the Jordan frame of $F(R)$ gravity. By linking Jordan- and Einstein-frame descriptions and deriving SR relations tailored to $F(R)$ models, the authors construct a Starobinsky-like inflation with higher-curvature corrections that achieves a positive running $ abla n_s$ while remaining consistent with a small tensor-to-scalar ratio. They provide a concrete example with an $R^5$-type extension that yields ACT-compatible values of the scalar tilt $n_s$ and running $ abla n_s$, and they extend the framework to a unified $F(R)$ description capable of PBH production and late-time DE. The approach preserves a purely gravitational origin of inflation, PBH phenomenology, and DE, and offers testable predictions for upcoming missions such as LiteBIRD and the Simons Observatory. Overall, the work presents a novel, ACT-consistent, Jordan-frame SR method and demonstrates its viability both for Starobinsky-like inflation and for broader unified cosmological scenarios.

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 $α_s$ 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 $α_s$ 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.