  Cosmological local observables are at best statistically determined by the
fundamental theory describing inflation. When the scalar inflaton is coupled
uniformly to a collection of subdominant massless gauge vectors, rotational
invariance is obeyed locally. However, the statistical isotropy of fluctuations
is spontaneously broken by gauge modes whose wavelength exceed our causal
horizon. This leads to a landscape picture where primordial correlators depend
on the position of the observer. We compute the stochastic corrections to the
curvature power spectrum, show the existence of a new local observable (the
shape of the quadrupole), and constrain the theory using Planck limits.
