Induced stochastic gravitational-wave background non-Gaussianities from primordial magnetic fields

This thesis aims to investigate the non-Gaussian features of a stochastic gravitational- wave background sourced by primordial magnetic fields generated during inflationary era. Such fields can be significantly amplified on small scales in some magnetogenesis scenarios while remaining compatible with CMB bounds on large scales, making the associated gravitational wave signal potentially accessible to future detectors. Even if the magnetic field is assumed to have Gaussian statistics, its anisotropic energy- momentum tensor can still induce non-Gaussian features in the spin-2 gravitational- wave background. This motivates the study of higher-order correlators as a way to extract information on the physical mechanism responsible for the production of the GW signal, helping to provide new insights into the fundamental physics of the early Universe. After reviewing the computation of the gravitational-wave power spectrum sourced by primordial magnetic fields, we extend the analysis to the connected four-point function of tensor modes, namely the primordial GW trispectrum. In our bench- mark setup, the trispectrum can be written into the product of time and momentum integrals, which makes the calculation tractable and highlights a stationarity con- dition in the late-time contributions. The resulting signal is naturally associated with folded momentum configurations. We evaluate a representative contribution to the connected trispectrum in the case of a delta-function magnetic power spec- trum source. This work offers an initial illustration of magnetically induced GW non-Gaussianities, and provides a starting point for extending the analysis to more realistic source spectra and for exploring observational prospects with pulsar timing arrays and next-generation gravitational-wave experiments.