Gravitational wave anisotropies from axion inflation

An important prediction of inflation is the production of a primordial stochastic gravitational wave background. Observing this background is challenging due to the weakness of the signal and the simultaneous presence of an astrophysical background generated by many unresolved late-time sources. One possible way to distinguish between the two is to examine their anisotropies. In this paper we calculate the primordial correlation function of gravitational wave anisotropies in the cosmological background generated by axion inflation, where the inflaton is a pseudo-Nambu-Goldstone boson coupled to gauge fields. In this scenario, tensor modes arise not only from the standard amplification of vacuum fluctuations present in any inflationary model, but also from the inverse decay process of the produced gauge fields. The correlator of gravitational wave anisotropies consists therefore of two main components: the contribution from vacuum tensor modes and the contribution from tensor modes sourced by the gauge fields. Our analysis shows that, while the former, previously studied in the literature, is negligible, the one arising from the sourced tensor modes, normalized by the fractional energy density at interferometer frequencies, can reach values as large as $\mathcal{O}(10^{-1})$. This result shows that axion inflation can generate large anisotropies with the potential to be observed by gravitational wave detectors within a reasonable time frame.