Statistics of Anisotropies in Inflation with Spectator Vector Fields

Abstract

We study the statistics of the primordial power spectrum in models where massless gauge vectors are coupled to the inflaton, paying special attention to observational implications of having fundamental or effective horizons embedded in a bath of infrared fluctuations. As quantum infrared modes cross the horizon, they classicalize and build a background vector field. We find that the vector experiences a statistical precession phenomenon. Implications for primordial correlators and the interpretation thereof are considered. Firstly, we show how in general two, not only one, additional observables, a quadrupole amplitude and an intrinsic shape parameter, are necessary to fully describe the correction to the curvature power spectrum, and develop a unique parametrization for them. Secondly, we show that the observed anisotropic amplitude and the associated preferred direction depend on the volume of the patch being probed. We calculate non-zero priors for the expected deviations between detections based on microwave background data (which probes the entire Hubble patch) and large scale structure (which only probes a fraction of it).