Cosmological consequences of statistical inhomogeneity

TL;DR

This paper explores the implications of a space-dependent primordial mean of scalar perturbations, constructed from an alternative quantum state, and assesses its compatibility with current and future cosmological observations.

Contribution

It introduces a model with a space-dependent primordial mean derived from a coherent quantum state and analyzes its cosmological signatures and observational constraints.

Findings

Current data does not favor a primordial mean over large scales.

Strong constraints from Planck bispectrum data.

Future observations like CMB $d$-distortion could test small-scale hypotheses.

Abstract

A space-dependent mean for cosmological perturbations negates the ansatz of statistical homogeneity and isotropy, and hence ergodicity. In this work, we construct such a primordial mean of scalar perturbations from an alternative quantum initial state (coherent state) and examine the associated power and bi-spectra. A multitude of cosmological tests based on these spectra are discussed. We find that current cosmological data doesn't favor a primordial mean over large scales and strong constraints arise from the limit on bispectrum from Planck data. At small scales, this hypothesis can be tested by future observables such as $\mu$-distortion of CMB.