Signatures of graviton mass on the Stochastic Gravitational-Wave Background and implications for interferometers

Although astrophysical observations put strong constraints on the graviton mass in late Universe, there is still room for gravitons to acquire an heavy mass during its early stages. In this thesis we study the effect of a massive graviton on the Stochastic Gravitational Wave Background (SGWB) of Cosmological origin. At early time we consider a scenario where graviton mass during inflation originates, in an effective field theory approach, from a primordial mechanism of spontaneous symmetry breaking of space-diffeomorphisms; at late time instead it is considered a recent theory of massive gravity developed by De Felice and Mukohyama which minimally modifies the de Rham-Gabadadze-Tolley (dRGT) theory, and where the assumption of a Lorentz symmetry violation allows the propagation of only two tensor massive modes and ensures the stability of the solution on a Friedmann–Lema\^{i}tre–Robertson–Walker (FLRW) background. Whereas the light graviton mass in late time modifies the graviton geodesics during its propagation, the heavy mass at early times strongly affects the primordial tensor power spectrum, pushing it toward a more blue tilt. Both these effects may leave distinct signatures on the angular correlators of the SGWB energy density. The analysis of the angular power spectrum is firstly performed analytically, and then numerically exploiting the publicly available code Cosmic Linear Anisotropy Solving System (CLASS), revealing different visible signatures arising from the graviton mass on early and late times on the large and medium scales between l ~2 and l ~100; this multipole domain overlaps with the range of scales where future interferometers as LISA and ET are expected to work, opening the doors for an exciting future. We have also explored the role of the graviton mass on the three-point function of the SGWB energy density, focusing both on primary and secondary non-Gaussianity effects.