Translational invariance and the anisotropy of the cosmic microwave background

Primordial quantum fluctuations produced by inflation are conventionally assumed to be statistically homogeneous, a consequence of translational invariance. In this paper we quantify the potentially observable effects of a small violation of translational invariance during inflation, as characterized by the presence of a preferred point, line, or plane. We explore the imprint such a violation would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes ⟨aₗₘa_l^'m^'*⟩ of the spherical-harmonic coefficients.