Inflation in non-minimal matter-curvature coupling theories

TL;DR

This paper explores how non-minimal matter-curvature coupling affects inflation, altering the dynamics and primordial perturbation spectrum, and derives observational constraints from Planck data.

Contribution

It introduces modifications to inflationary models with non-minimal matter-curvature coupling and analyzes their observational implications and constraints.

Findings

Modified Friedmann equation at high energy densities

Distinct consistency relation between tensor-to-scalar ratio and spectral index

Planck data constrains the non-minimal coupling scale

Abstract

We study inflationary scenarios driven by a scalar field in the presence of a non-minimal coupling between matter and curvature. We show that the Friedmann equation can be significantly modified when the energy density during inflation exceeds a critical value determined by the non-minimal coupling, which in turn may considerably modify the spectrum of primordial perturbations and the inflationary dynamics. In particular, we show that these models are characterised by a consistency relation between the tensor-to-scalar ratio and the tensor spectral index that can differ significantly from the predictions of general relativity. We also give examples of observational predictions for some of the most commonly considered potentials and use the results of the Planck collaboration to set limits on the scale of the non-minimal coupling.