Production and detection of relic gravitons in quintessential inflationary models

A large class of quintessential inflationary models, recently proposed by Peebles and Vilenkin, leads to post-inflationary phases whose effective equation of state is stiffer than radiation. The expected gravitational waves logarithmic energy spectra are tilted towards high frequencies and characterized by two parameters: the inflationary curvature scale at which the transition to the stiff phase occurs and the number of (non conformally coupled) scalar degrees of freedom whose decay into fermions triggers the onset of a gravitational reheating of the Universe. Depending upon the parameters of the model and upon the different inflationary dynamics (prior to the onset of the stiff evolution) the relic gravitons energy density can be much more sizeable than in standard inflationary models, for frequencies larger than 1 Hz. We estimate the required sensitivity for detection of the predicted spectral amplitude and show that the allowed region of our parameter space leads to a signal smaller (by one 1.5 orders of magnitude) than the advanced LIGO sensitivity at a frequency of 0.1 KHz. The maximal signal, in our context, is expected in the GHz region where the energy density of relic gravitons in critical units (i.e. $h_0^2 \Omega_{GW}$) is of the order of $10^{-6}$, roughly eight orders of magnitude larger than in ordinary inflationary models. Smaller detectors (not necessarily interferometers) can be relevant for detection purposes in the GHz frequency window. We suggest/speculate that future measurements through microwave cavities can offer interesting perspectives.