• pulsar timing array
• stochastic background
• scalar-induced
• cosmology
• gravitational waves

This Master's Degree thesis focuses on the Scalar-Induced Gravitational Wave Background generated by large primordial scalar and tensor fluctuations, which couple at second order in Cosmological Perturbation Theory. These gravitational waves re-entered the horizon during the Radiation-Dominated (RD) phase and can peak in the Pulsar Timing Array (PTA) frequency band around 10^{-9}-10^{-8} Hz. We considered the scalar-scalar and the scalar-tensor seeds,  but excluding the tensor-tensor contribution since it is negligible.
We computed the resultant GW spectral energy density per logarithmic frequency interval at the time of emission and today, focusing on PTA scales, for both scalar-scalar and scalar-tensor.
While the scalar-scalar source is widely studied in literature, accurate mixed term studies were still lacking: the work goes in depth with the scalar-tensor  term, deriving analytically the power spectrum and numerically the corresponding GW spectral energy density. We find that in certain ranges of frequency, the scalar-tensor term gives a larger contribution to the sum of the two signals.
Plotting the latter against the NANOGrav sensitivity curve, we find that the SIGWs may become a potential target for PTA detectors.