  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.
