Born–Infeld-type modified gravity

Abstract

We propose and investigate the modified Born–Infeld-type gravity model with the function [Formula: see text]. At different values of the dimensionless parameter [Formula: see text], the action is converted into some models including general relativity ([Formula: see text]), the Starobinsky model ([Formula: see text]), the exponential model of gravity ([Formula: see text]), and a model proposed in [S. I. Kruglov, Born–Infeld-like modified gravity, Int. J. Theor. Phys. 52 (2013) 2477–2484; S. I. Kruglov, Notes on Born–Infeld-like modified gravity, Astrophys. Space Sci. 361 (2016) 73] ([Formula: see text]). A bound on the parameters, [Formula: see text][Formula: see text]cm2, are due to local tests. The constant curvature solutions are obtained, and we found the potential, and the mass of the scalaron in the Einstein frame. The model describes the inflation of the universe. The de Sitter spacetime is unstable and a Minkowski spacetime is stable. We investigate the cosmological parameters and some critical points of autonomous equations.