Primordial black holes formation in new inflationary F(R) gravity models

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.