Probing the speed of scalar-induced gravitational waves with pulsar timing arrays

Recently, several regional pulsar timing array collaborations, including CPTA, EPTA, PPTA, and NANOGrav, have individually reported compelling evidence for a stochastic signal at nanohertz frequencies. This signal originates potentially from scalar-induced gravitational waves associated with significant primordial curvature perturbations on small scales. In this letter, we employ data from the EPTA DR2, PPTA DR3, and NANOGrav 15-year data set, to explore the speed of scalar-induced gravitational waves using a comprehensive Bayesian analysis. Our results suggest that, to be consistent with pulsar timing array observations, the speed of scalar-induced gravitational waves should be $c_g\gtrsim 0.61$ at a $95\mathrm{\%}$ credible interval for a lognormal power spectrum of curvature perturbations. Additionally, this constraint aligns with the prediction of general relativity that $c_g=1$ within a $90\mathrm{\%}$ credible interval. Our findings underscore the capacity of pulsar timing arrays as a powerful tool for probing the speed of scalar-induced gravitational waves.