Cosmology of unimodular Born–Infeld-[formula omitted] gravity

Abstract

We propose a novel modified gravity: unimodular generalization of the Born–Infeld-f(R) gravity within the framework of cosmology. After formulating the action corresponding to the generalized Born–Infeld-f(R) gravity, we present a reconstruction scheme of this unimodular extension to achieve various cosmological eras of the universe. Interestingly, the unimodular generalization of Born–Infeld-f(R) gravity proves to be suitable for inflation (de-Sitter and quasi de-Sitter) along with power law cosmology which actually includes from reheating to the Standard Big-Bang cosmology. Apart from the inflation, such generalized Born–Infeld-f(R) theory is also capable to trigger non-singular bouncing cosmology for suitable forms of the unimodular Lagrange multiplier, which are exotic for the standard Einstein–Hilbert gravity and cannot be realized in that case. The possible consequences are discussed.