Correlated scalar perturbations and gravitational waves from axion inflation

The scalar and tensor fluctuations generated during inflation can be correlated, if arising from the same underlying mechanism. In this paper we investigate such correlation in the model of axion inflation, where the rolling inflaton produces quanta of a $U(1)$ gauge field which, in turn, source scalar and tensor fluctuations. We compute the primordial correlator of the curvature perturbation, $\zeta$, with the gravitational energy density, $\Omega_{GW}$, at frequencies probed by gravitational wave detectors. This two-point function receives two contributions: one arising from the correlation of gravitational waves with the scalar perturbations generated by the standard mechanism of amplification of vacuum fluctuations, and the other coming from the correlation of gravitational waves with the scalar perturbations sourced by the gauge field. Our analysis shows that the former effect is generally dominant. For typical values of the parameters, the correlator, normalized by the amplitude of $\zeta$ and by the fractional energy in gravitational waves at interferometer frequencies, turns out to be of the order of $10^{-4}\div 10^{-2}$.