Translational Invariance and the Anisotropy of the Cosmic Microwave Background

TL;DR

This paper investigates how slight violations of translational invariance during inflation could leave detectable signatures in the cosmic microwave background anisotropy, providing explicit formulas for these effects.

Contribution

It introduces a quantitative framework to analyze the observable consequences of translational invariance violations in the early universe.

Findings

Derived explicit formulas for CMB anisotropy coefficients affected by invariance violations

Identified potential observable imprints of preferred points, lines, or planes during inflation

Quantified the amplitude of anisotropy deviations from standard models

Abstract

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 $<a_{lm}a_{l'm'}^*>$ of the spherical-harmonic coefficients.