Towards a proof of the equivalence between FRW background expansion and statistical isotropy

TL;DR

This paper explores the potential equivalence between the universe's background expansion during inflation and the statistical isotropy of primordial curvature perturbations, motivated by anomalies in CMB data suggesting a preferred direction.

Contribution

It advances towards a proof of the theoretical equivalence between FRW background expansion and statistical isotropy of primordial perturbations during inflation.

Findings

Progress towards a formal proof of equivalence

Insights into the connection between inflation and CMB anomalies

Implications for understanding universe's isotropy

Abstract

We will expose in this paper our advances towards a proof of the equivalence between FRW background expansion, during some period of time that contains primordial inflation, and the statistical isotropy of the primordial curvature perturbation $\zeta$ at the end of this period of time. Our motivation rests on the growing interest in the existence of a preferred direction in the Universe hinted by the continuous presence of anomalies in the CMB data.