Search for a Gravitational-Wave Background from Sound Speed Resonance from Advanced LIGO and Advanced Virgo's First Three Observing Runs

We search for a stochastic gravitational-wave background (SGWB) originating from scalar-induced gravitational waves (SIGWs) with the sound speed resonance (SSR) effect using data from Advanced LIGO and Advanced Virgo’s first three observing runs. The SSR mechanism, characterized by an oscillating sound speed squared term, can induce a nonperturbative parametric amplification of specific perturbation modes during inflation, leading to enhanced primordial curvature perturbations and a significant SIGW signal. We perform a Bayesian analysis to constrain the model parameters describing the SGWB spectrum from the SSR effect. Our results show no statistically significant evidence for the presence of such a signal in the current data. Consequently, we place an upper limit of $\mathrm{\mid }{\tau }_0\mathrm{\mid }\lesssim 5.9\times {10}^3\mathrm{s}$ at $95\mathrm{\%}$ confidence level on the start time of the oscillation in the SSR model. These results demonstrate the capability of current gravitational wave detectors to probe inflation models through the SSR mechanism and paves the way for future searches with improved sensitivity.