Eur. Phys. J. C (2015) 75: 111
https://doi.org/10.1140/epjc/s10052-015-3332-x

Regular Article - Theoretical Physics

Chaotic inflation in higher derivative gravity theories

Department of General and Theoretical Physics, Eurasian Center for Theoretical Physics, Eurasian National University, Astana, 010008, Kazakhstan

^* e-mail: l.sebastiani@science.unitn.it

Received: 10 January 2015
Accepted: 25 February 2015
Published online: 7 March 2015

Abstract

In this paper, we investigate chaotic inflation from a scalar field subjected to a potential in the framework of -gravity, where we add a correction to Einstein’s gravity based on a function of the square of the Ricci scalar , the contraction of the Ricci tensor , and the contraction of the Riemann tensor . The Gauss–Bonnet case is also discussed. We give the general formalism of inflation, deriving the slow-roll parameters, the -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.