Investigating cosmic histories with a stiff era through gravitational waves

We investigate the potential of gravitational-wave background searches to constrain cosmic histories characterized by a stiff equation of state, preceded by a period of matter domination. Such a scenario leads to a characteristic peak in the primordial gravitational-wave spectrum originating from cosmological inflation. Assuming instant transitions between distinct epochs, which allows for an analytical treatment of the gravitational-wave spectrum, we perform a Bayesian inference analysis to derive constraints from the first three observing runs of the LIGO-Virgo-KAGRA Collaboration. Additionally, we consider a smooth transition, employing an axionlike particle physics model, and highlight the differences compared to the instant transition approximation. Finally, we forecast detection prospects for such a cosmic history through future gravitational-wave experiments.