w, H_{\rm inf}, f_{\rm RD}\rbrace$, as these control both the duration of the stiff period and the shape of the GW spectrum (and hence the energy carried by the GWs). As we will see, these constraints will restrict severely the ability of detectors to observe the blue tilted GW background due to an SD epoch. We find that the above constraints render the signal completely inaccessible to the observational window of aLIGO, independently of the parameter space. Whilst the background remains detectable by LISA, it is only observable if the inflationary scale is as large as $H_{\rm inf} \gtrsim 10^{13}$ GeV (corresponding to at least $\mathcal{O}(10)\%$ of its current upper bound), $f_{\rm RD}$ lies in the range $10^{-11}~{\rm Hz} \lesssim f_{\rm RD} \lesssim 3.6\cdot10^{-9}~{\rm Hz}$, or equivalently the Universe becomes RD at sufficiently low temperatures $1~{\rm MeV} \lesssim T_{\rm RD} \lesssim 150$ MeV (i.e. the SD spoch spans many decades in energy scale), and the stiff EoS is confined within the narrow range $0.46 \lesssim w \lesssim 0.56$. This corresponds to a small island in the parameter space .

The paper is divided as follows. In Section \[sec:Inflation\], we briefly review the form of the spectrum of GWs from inflation. 