Cosmic Microwave Background Spectral Distortions and Primordial Gravitational Waves

Distortions of the Cosmic Microwave Background (CMB) spectrum in the frequency domain provides a new window onto a variety of cosmological phenomena, including the physics of the early Universe. These distortions are tiny departures of the CMB frequency spectrum from a pure blackbody which are created whenever the energy or the number density of the CMB photons is changed and therefore encode information about the thermal history of the Universe. They can be produced by a number of processes occurring at the early stages of cosmic history and therefore allow us to probe the standard picture of cosmology. Spectral distortions are created by processes that drive matter and radiation out of equilibrium. This could be related to early energy injection. Depending on the moment of injection, this causes a distortion which can be of two main types, namely the so called µ and y-type distortions. The standard cosmological model predicts the production of CMB spectral distortions, thanks to various effects, one of which is the dissipation of acoustic waves of the photon-baryon plasma through the Silk damping effect. Such distortions can be used to constrain the power of the primordial density perturbations arising from inflation in the range . Moreover, this work will include an original part focused on the possibility of generating statistically anisotropic features in the CMB spectral distortions and on sources of these anisotropic features. Within many candidates, there are the so called inflationary fossils, models in which the scalar field driving inflation couples to a new primordial degree of freedom. In particular, tensor fossils refer to long wavelength relic gravitational waves from inflation that produce a quadrupolar modulation of curvature perturbations. The tensor fossils no longer interact, or interact very weakly, during late time cosmic evolution. Therefore, the unique observational effect due to the coupling with the inflaton field would be to give rise to local departures from statistical isotropy in the primordial curvature perturbation field. The original contribution of this Thesis will consist in the study of how this new tensor degree of freedom can distort the primordial scalar curvature two point correlation function. In order to evaluate this, the mixed bispectrum involving tensor scalar scalar fluctuations will be computed in the so called squeezed limit configuration, which gives rise to an anisotropic power spectrum of curvature (density) perturbations. Hence, in this work, we delve into CMB spectral distortions, pointing out the main features and their importance. We derive the cross correlation between CMB anisotropies and CMB spectral distortions, which is a useful observable to constrain primordial non Gaussianity. We then focus on the study of the imprints of the tensor fossils on cosmic structures. We will see how tensor fossils can leave a signature in the CMB spectral distortions, by evaluating the ensemble average of the µ distortion modulated by the long wavelength tensor mode. Then, we will also compute the corresponding cross correlation between CMB anisotropies and µ distortions, computing the tensor scalar scalar and the scalar tensor tensor bispectra, both in the case of modulation.