# Post-inflationary phases stiffer than radiation and Palatini formulation

## TL;DR

This paper explores how quadratic modifications to gravity in the Palatini formulation influence the evolution and observational signatures of quintessential inflation, particularly suppressing tensor modes and relic graviton signals.

## Contribution

It demonstrates that quadratic gravity in the Palatini formulation allows certain inflationary models to remain viable by suppressing tensor modes and relic graviton signals.

## Key findings

- Quadratic gravity suppresses tensor-to-scalar ratio in Palatini formulation.
- Power-law potentials remain viable with quadratic corrections.
- Relic graviton spectrum is significantly suppressed.

## Abstract

If the inflaton and the quintessence fields are identified, the background geometry evolves through a stiff epoch undershooting the expansion rate of a radiation-dominated plasma. For some classes of inflationary potentials this scenario is at odds with the current observational evidence since the corresponding tensor-to-scalar ratio is too large. Quintessential inflation is analyzed when the gravitational action is supplemented by a contribution quadratic in the Einstein-Hilbert term. In the Palatini formulation the addition such a term does not affect the scalar modes during the inflationary phase and throughout the course of the subsequent stiff epoch but it suppresses the tensor power spectrum and the tensor-to-scalar ratio. While in the Palatini formulation the power-law potentials leading to a quintessential inflationary dynamics are again viable, the high-frequency spike of the relic graviton spectrum is squeezed and the whole signal is suppressed at least when the higher-order contributions appearing in the action are explicitly decoupled from the inflaton.