Spikes in the relic graviton background from quintessential inflation

The energy spectra of gravitational waves (GWs) produced in quintessential inflationary models increase in frequency and exhibit a sharp spike around 170 GHz where the associated fraction of critical energy density presently stored in relic gravitons is of the order of 10 -6 . The maximal energy density present (today) in the stochastic GW background of quintessential origin is mainly constrained by the consistency with the (homogeneous and isotropic) big-bang nucleosynthesis scenario. We contrast our findings with the spectra of ordinary inflationary models and we comment on possible detection strategies for the spike.