Inflation in <i>F</i> ( <i>R</i> ) gravity models revisited after ACT

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.