Chaotic inflation in higher derivative gravity theories

TL;DR

This paper explores chaotic inflation within higher derivative gravity theories, deriving formalism and analyzing specific models to assess their viability against observational data.

Contribution

It introduces a formalism for inflation in $f(R^2, P, Q)$-gravity and examines explicit models, including massive and quartic scalar fields, to evaluate their observational viability.

Findings

Derived slow-roll parameters and spectral indexes in $f(R^2, P, Q)$-gravity.

Analyzed specific models with massive and quartic scalar potentials.

Identified models consistent with observational constraints.

Abstract

In this paper, we investigate chaotic inflation from scalar field subjected to potential in the framework of $f(R^2, P, Q)$-gravity, where we add a correction to Einstein's gravity based on a function of the square of the Ricci scalar $R^2$, the contraction of the Ricci tensor $P$, and the contraction of the Riemann tensor $Q$. The Gauss-Bonnet case is also discussed. We give the general formalism of inflation, deriving the slow-roll parameters, the $e$-folds number, and the spectral indexes. Several explicit examples are furnished, namely we will consider the cases of massive scalar field and scalar field with quartic potential and some power-law function of the curvature invariants under investigation in the gravitational action of the theory. Viable inflation according with observations is analyzed.