Extensions of the Starobinsky R^2 inflationary model

We study several extensions of the Starobinsky model of inflation, which obey all observational constraints on the inflationary parameters, by demanding that both the inflaton scalar potential in the Einstein frame and the F(R) gravity function in the Jordan frame have the explicit dependence upon fields and parameters in terms of elementary functions. Our models are continuously connected to the original Starobinsky model via changing the parameters. We modify the Starobinsky (R + R2) model and calculate the inflationary observables and the allowed limits on the deformation parameters by using the latest observational bounds. The talk is based on the paper V.R. Ivanov, S.V. Ketov, E.O. Pozdeeva, S.Yu. Vernov, JCAP 03 (2022) 058 and recent investigations.