The quest of CMB spectral distortions to probe the scalar-induced gravitational wave background interpretation in PTA data

Gravitational Waves (GW) sourced by second-order primordial curvature fluctuations are among the favoured models fitting the recent Pulsar Timing Array (PTA) measurement of a Stochastic GW Background (SGWB). We study how spectral distortions (SDs) and anisotropies of the Cosmic Microwave Background (CMB) can constrain such scalar fluctuations. Whereas COBE FIRAS data have no sufficient sensitivity to probe the PTA lognormal hypothesis, we show how future PIXIE-like experiments can detect the CMB SDs from the scalar-induced interpretation of the SGWB in PTA data. We finally show how the transformative synergy between PTA data and future CMB SD measurements is important for reconstructing primordial fluctuations at these small scales.