Erratum: Statistical anisotropy in the inflationary universe

TL;DR

This paper corrects a previous calculation showing that single-field inflationary models cannot produce detectable statistical anisotropy in the power spectrum, significantly reducing earlier estimates of its magnitude.

Contribution

It provides a corrected analysis demonstrating that statistical anisotropy in single-field inflation is much smaller than previously thought, below detectable levels.

Findings

Corrected the amplitude of scalar perturbations after Hubble crossing

Reduced the estimated anisotropy level from 10^{-2} to 10^{-6}

Concluded single-field inflation cannot produce observable anisotropy

Abstract

An error was made when calculating the amplitude of the perturbed scalar mode after Hubble-radius crossing. When corrected, it eliminates the leading term in the statistical anisotropy of the power spectrum, reducing it from the previously claimed upper estimate of $\lesssim 10^{-2}$ to the level of at most $10^{-6}$, which is beyond the possibility of detection. The general conclusion is that a single-field inflationary scenario cannot produce statistical anisotropy of appreciable magnitude.