Probing primordial non-Gaussianity via cosmological gravitational wave anisotropies

In modern Cosmology, primordial non-Gaussianity (PNG) is regarded as a fundamental and independent source of information about the physics of the early Universe. The ideal observable to measure the non-Gaussian nature of primordial perturbations, and its eventual scale dependence, is the cosmic microwave background (CMB) radiation. In this work another promising probe of primordial non-Gaussianity is considered, namely the cosmological gravitational wave background (CGWB) generated during inflation. An eventual detection of such a GW background in the near future may possibly provide with new and exciting information, inaccessible to CMB measurements. Signatures of primordial non-Gaussianity are in fact expected to be picked up via the GW propagation across large- scale scalar perturbations. Particular attention is given to the CGWB energy density anisotropies 3- point angular correlator, or bispectrum, as the lowest-order indicator of the presence of PNG. Explicit expressions can be derived in the case non-Gaussianity is parametrized in terms of the local ansatz for the primordial curvature perturbation. The inclusion of the scale dependence, or running, in the discussion is then achieved by means of a kernel approach for the non-linear parameter fNL and of a subsequent matching with bispectrum templates recurring in the literature. A specific scenario of CGWB sourced at second order from enhanced small-scale scalar perturbations, arising with the formation of primordial black holes (PBHs), is also considered. In this context the presence of primordial non-Gaussianity would show up already at the emission, as an initial condition. The PBHs mass is taken to be such that they may as well comprise all of the dark matter (DM). If this was actually the case it would be remarkable, in presence of a sufficient running of non-Gaussianity, the possibility to obtain an arbitrarily anisotropic CGWB which is otherwise, in the non-running scenario, constrained to be highly isotropic due to cold dark matter isocurvature (CDI) bounds.