# Relic gravitational waves from Quintessential Inflation

## TL;DR

This paper investigates relic gravitational waves produced in quintessential inflation, highlighting a kinetic regime after inflation that leads to a blue spectrum and discussing detection prospects with advanced gravitational wave observatories.

## Contribution

It provides a model-independent analysis of gravitational wave production in quintessential inflation and demonstrates a concrete potential that fits observational constraints.

## Key findings

- Kinetic regime after inflation results in a blue gravitational wave spectrum.
- Instant preheating can produce the required post-inflation temperature.
- Detection prospects are discussed for LIGO and LISA.

## Abstract

We study relic gravitational waves in the paradigm of quintessential inflation. In this framework, irrespective of the underlying model, inflation is followed by the kinetic regime. Thereafter, the field energy density remains sub-dominant before the onset of acceleration. We carry out model independent analysis to obtain the temperature at the end of inflation and the estimate for upper bound on the Hubble parameter to circumvent the problem due to relic gravitational waves. In this process, we used Planck 2015 data to constrain the inflationary phase. We demonstrate that the required temperature can be produced by the mechanism of instant preheating. The generic feature of the scenario includes the presence of kinetic regime after inflation which results into blue spectrum of gravitational wave background at high frequencies. We discuss the prospects of detection of relic gravitational wave background in the advanced LIGO and LISA space-born gravitational wave missions. Finally we consider a concrete model to realize the paradigm of quintessential inflation and show that inflationary as well as post-inflationary evolution can successfully be described by the inflaton potential, $V(\phi) \propto Exp(-\lambda \phi^n/\Mpl^n)(n>1)$, by suitably constraining the parameters of the model.