Testing Axion Inflation with Cosmological Gravitational Wave Anisotropies

Gravitational Waves (GWs) represent a new window into the Universe. Through the detections of GWs from astrophysical compact objects, primarily binary black holes and neutron stars, by the LIGO-Virgo-KAGRA collaboration, we have gained significant insights into astrophysics and fundamental physics. The next target for GW detectors is the gravitational wave background (GWB), which has recently been claimed to be detected by the NANOGrav collaboration. The GWB can arise from unresolved gravitational wave signals of astrophysical origin or result from early universe phenomena that rely on cosmological mechanisms of production. Both components are of fundamental importance in our understanding of the Universe. The study and detection of GWB astrophysical counterparts would enhance our understanding of galactic and extra- galactic populations of astrophysical objects. On the other hand, the cosmological GWB would allow us to probe the Universe during its early stages, up to the quantum wall, which cannot be explored through other means. Furthermore, detecting the GWB would also provide insights into new physics beyond the Standard Model, enabling also tests of the Λ Cold Dark Matter (ΛCDM) cosmological model. Future third-generation ground-based GW interferometers, such as the Einstein Telescope (ET) and Cosmic Explorer (CE), along with space-based detectors like LISA, BBO, and DECIGO, offer promising prospects for detecting the stochastic GWB. These detectors will employ advanced technological strategies to reduce noise and enhance angular sensitivity, enabling them to cover frequency bands influenced by various sources of the SGWB, both astrophysical and cosmological. Given the expected richness of sources, if one is interested in testing new physics and cosmological models, it is necessary to find ways to disentangle among the various sources, resolved and unresolved, which overlap. A first attempt in distinguishing between the astrophysical and the cosmological contribution is given by reconstructing the gravitational waves frequency profile. However, what could really play a relevant role in sorting out all the different contributions are the SGWB anisotropies. For instance, we expect that astrophysical GWs reside mostly in galaxies, so they are distributed less isotropically with respect to cosmological ones. By going beyond the monopole (i.e., isotropic) term in the GW energy spectrum, one could retrieve information about a specific mechanism of production, spotting the peculiar signatures imprinted in the multipole (in a spherical harmonic expansion) contributions. Although it is expected that multipoles are suppressed by few orders of magnitude with respect to the monopole, in an optimal scenario of well understood noise and high SNR signals, it is possible to probe them up to ℓmax ≲ 15 − 20 with future interferometers (even higher when considering a detector network). This thesis work focuses on forecasting the GW spectrum and the angular power spectrum for an inflationary model never studied so far in this context - the axion-inflation model - which is considered as the prototype model for GW interferometer studies. It has been already shown that while features of the CGWB monopole depend heavily on the attributes of their generation mechanism, the CGWB anisotropy spectrum relies very weakly on the model. This is true as long as the initial conditions (IC) are are adiabatic. The CGWB can be affected by initial inhomogeneities related to some non-adiabatic IC. At present, literature lacks in considering this scenario, hence this study will fill a void in the current discussion on SGWB anisotropies from inflationary sources and consequent separability .