that the inflationary tensor tilt is expected to be only slightly-red tilted, according to the standard consistency condition \[c.f. Eq. (\[eq:consistencyCondition\])\]. A study in this spirit was initiated in [@Boyle:2005se; @Boyle:2007zx], but with the SD-to-RD energy scale fixed to its smallest possible value, $T_{\rm BBN}\sim 10^{-3}\text{ GeV}$, so that $f_{\rm RD}$ was fixed to its lowest possible value $f_{\rm BBN} \sim 10^{-11}$ Hz. In our present work we present a systematic exploration of the observability of the full parameter space $\lbrace w, H_{\rm inf}, f_{\rm RD}\rbrace$.

As a consistent cosmological history must preserve the success of BBN, we need to prevent the presence of a stiff epoch from changing significantly the expansion rate during BBN. There are two ways by which the latter can happen. First, if the stiff epoch does not end in time before the start of BBN the expansion rate would certainly deviate significantly from that of the $\Lambda$CDM. Second, even if RD starts in time, GWs should not carry too much energy, or otherwise the expansion rate during BBN (or CMB decoupling for this matter) would still be sufficiently altered. Thus, in order to be consistent with BBN/CMB, bounds must be put on the parameters $\lbrace 