Inflationary Perturbations in Palatini Generalised Gravity

TL;DR

This paper investigates how primordial perturbations are generated during inflation in generalized gravity theories using the Palatini approach, highlighting differences from the metric formalism in scalar and tensor perturbations.

Contribution

It compares Palatini and metric formalisms in f(R) and Scalar-Tensor theories, revealing distinct predictions for inflationary perturbations and spectral indices.

Findings

f(R) inflation does not produce suitable curvature perturbations

Scalar-Tensor theories generate nearly scalar invariant curvature perturbations

No tensor modes are produced in Scalar-Tensor theories

Abstract

We examine the generation of primordial perturbations during an inflationary epoch in generalised theories of gravity when the equations of motion are derived using the Palatini variational principle. Both f(R) and Scalar-Tensor theories are considered and we compare our results with those obtained under the conventional metric formalism. Non-linear generalisations of the action lead to different theories under the two variational choices and we obtain distinct results for scalar and tensor spectral indices and their ratio. We find the following general result; inflation driven solely by f(R) modifications alone do not result in suitable curvature perturbations whilst Scalar-Tensor theories generate nearly scalar invariant curvature perturbations but no tensor modes.