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 subdominant before the onset of acceleration. We carry out model-independent analysis to obtain the temperature at the end of inflation and the estimate for the upper bound on the Hubble parameter to circumvent the problem due to relic gravitational waves. In this process, we use 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 the kinetic regime after inflation, which results in the 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 postinflationary evolution can be successfully described by the inflaton potential, $V(\ensuremath{\phi})\ensuremath{\propto}\mathrm{Exp}(\ensuremath{-}\ensuremath{\lambda}{\ensuremath{\phi}}^{n}/{M}_{\mathrm{Pl}}^{n})(n>1)$, by suitably constraining the parameters of the model.