Cosmology with Pulsar Timing Array: the case of scalar-induced gravitational waves

Gravitational Waves (GWs) constitute a unique window on the very early universe, probing scales that are inaccessible even to Cosmic Microwave Background (CMB) experiments. Scalar-induced GWs represent a particular class of GWs which are sourced at second-order in perturbation theory whenever a scalar fluctuation of the metric is present. In this work we study the intuitive physics behind induced GWs and the construction of the power spectra, analyzing the imprints of local non-Gaussianity of the primordial curvature perturbation on the GW spectrum. For the first time we consider all the relevant non-Gaussian contributions up to third-order in the scalar seeds and we derive the related GW energy density ΩGW(k). We consider different types of primordial curvature power spectra and we assume radiation domination at the time of GW production. The goal of this work is to understand if these scalar-induced GWs and primordial non-Gaussianity can be probed by Pulsar Timing Array (PTA) experiments, which work in the nano-Hertz frequency range.