Constraining Modified Gravity with Large non-Gaussianities

TL;DR

This paper investigates how Gauss-Bonnet and axion-type curvature couplings in single field inflation models affect observable non-Gaussianities and gravitational waves, providing new constraints and potential signatures for cosmological observations.

Contribution

It introduces the effects of Gauss-Bonnet couplings on non-Gaussianities and gravitational waves in inflation, deriving constraints from observations and exploring specific models like DBI inflation.

Findings

Gauss-Bonnet term enhances gravitational wave production.

Large non-Gaussianities can be achieved with smaller sound speeds.

Constraints on parameters from WMAP data are established.

Abstract

In writing a covariant effective action for single field inflation, one is allowed to add a Gauss-Bonnet and axion-type curvature couplings. These couplings represent modifications of gravity, and are the unique higher-curvature terms that lead to second order equations of motion in four dimensions. In this paper we study the observational consequences of such couplings for models with large non-gaussianities. Our focus is on the Gauss-Bonnet term. In particular, we study an effective action where the scalar Lagrangian is a general function of the inflaton and its first derivative. We show that, for large non-gaussianities, one can write $f_{NL}$ in terms of only three parameters. The shape of $f_{NL}$ is also studied, and we find that it is very similar to that of k-inflation. We show that the Gauss-Bonnet term enhances the production of gravitational waves, and allows a smaller speed of sound for scalar perturbations. This, in turn, can lead to larger non-gaussianities which can be constrained by observations. Using current WMAP limits on $f_{NL}$ and the tensor/scalar ratio, we put constraints on all parameters. As an example, we show that for DBI inflation, the Gauss-Bonnet coupling leads to an interesting observational window with both large $f_{NL}$ and a large amplitude of gravitational waves. Finally, we show that the Gauss-Bonnet coupling admits a de-Sitter phase with a relativistic dispersion relation for scalar perturbations.