Chaotic inflation in higher derivative gravity theories

Abstract

In this paper, we investigate chaotic inflation from a scalar field subjected to a potential in the framework of (Formula presented.)-gravity, where we add a correction to Einstein’s gravity based on a function of the square of the Ricci scalar (Formula presented.), the contraction of the Ricci tensor (Formula presented.), and the contraction of the Riemann tensor (Formula presented.). The Gauss–Bonnet case is also discussed. We give the general formalism of inflation, deriving the slow-roll parameters, the (Formula presented.)-fold number, and the spectral indices. Several explicit examples are furnished; namely, we will consider the cases of a massive scalar field and a scalar field with quartic potential and some power-law function of the curvature invariants under investigation in the gravitational action of the theory. A viable approach to inflation according with observations is analyzed.