  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).
