Abstract:
The F(R) gravity models of inflation have been revisited in light of recent observations of cosmic microwave background radiation from the Atacama Cosmology Telescope and the DESI collaboration. A detailed study of the evolution equations in the Jordan frame has been with a new slow-roll approximation for F(R)-gravity inflationary models has been 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. Using the proposed slow-roll approximation in the Jordan frame, we provide a new F(R) gravity modification of the Starobinsky inflationary model, which satisfies all ACT constraints. An F(R)-gravity model that unifies inflation and production of primordial black holes is also proposed. The talk in based on the paper by S.V. Ketov, E.O. Pozdeeva, and S.Yu. Vernov, arXiv:2508.08927.
