Can tensor-scalar induced GWs dominate PTA observations?

Observational constraints on small-scale primordial gravitational waves are considerably weaker than those on large scales. We focus on scenarios with significant primordial gravitational waves and curvature perturbations on small scales, studying the energy density spectrum of the second-order tensor-scalar induced gravitational wave (TSIGW). By leveraging current data from cosmic microwave background (CMB), baryon acoustic oscillations (BAO), and pulsar timing array (PTA), combined with the signal-to-noise ratio (SNR) analysis of Laser Interferometer Space Antenna (LISA), we can investigate how tensor-scalar induced gravitational waves affect observations on various scales, thus constraining the parameter space for primordial gravitational waves and curvature perturbations. The Bayes factor analysis suggests that tensor-scalar induced gravitational wave (TSIGW)+primordial gravitational wave (PGW) might be more likely to dominate current pulsar timing array (PTA) observations compared to supermassive black hole binary (SMBHB).