Cosmological observables, infrared growth of fluctuations, and scale-dependent anisotropies

We simplify and extend semiclassical methods in inflationary cosmology that capture leading IR corrections to correlators. Such IR effects can be absorbed into a coordinate change when examining sufficiently local observables, but not when comparing observations at large separation in scales, such as seen by a late-time observer. The analysis is facilitated by definition of a scale-dependent metric and physical momentum. These assist definition of IR-safe observables seen by a postinflationary observer, which are contrasted to those based on the local geometry of the reheating surface. For the former observables, the observer's horizon provides an effective IR cutoff. IR growth of fluctuations contributes to enhanced statistical inhomogeneities/anisotropies at short scales, observation of which by a present-day observer might be sought in 21 cm measurements. Such IR corrections are argued to become large for a very late-time observer.