New one-parametric extension of the Starobinsky inflationary model

Abstract

We propose a one-parametric extension of the Starobinsky $R+R^2$ model by adding the $\left(R+m^2\beta^2\right)^{3/2}$ term. The parameter $m$ is the inflaton mass, which is determined in the same way as in the Starobinsky model, and $\beta$ is a dimensionless constant. Using the Einstein frame and the scalar field potential, we get the inflationary parameters of the model proposed. The value of the tensor-to-scalar ratio $r$ can be significantly larger than in the Starobinsky model. The considered inflationary model is in a good agreement with the current observational data. The corresponding scalar field potential is a polynomial of the exponential function.

Black hole shadows in Einstein-Bel-Robinson gravity*

“…The Starobinsky gravity model [58], one of the first f(R) models, is perfectly compatible with cosmological inflation [59]. In 2022, Ketov extended this model perturbatively with quartic curvature terms that are structurally connected to the Bel-Robinson tensor [60,61] in four dimensions [62].…”