Dominance of gauge artifact in the consistency relation for the primordial bispectrum

TL;DR

This paper shows that when considering gauge-invariant variables based on our observable universe, the expected consistency relation for the primordial bispectrum in the squeezed limit does not hold, revealing a gauge artifact dominance.

Contribution

It demonstrates that the conventional consistency relation for the bispectrum is dominated by gauge artifacts when using genuinely gauge-invariant variables based on the local observable universe.

Findings

The leading term of the bispectrum in the squeezed limit vanishes for gauge-invariant variables.

The usual consistency relation is invalidated by gauge artifacts in the local universe.

The result emphasizes the importance of gauge considerations in cosmological perturbation theory.

Abstract

The conventional cosmological perturbation theory has been performed under the assumption that we know the whole spatial region of the universe with infinite volume. This is, however, not the case in the actual observations because observable portion of the universe is limited. To give a theoretical prediction to the observable fluctuations, gauge-invariant observables should be composed of the information in our local observable universe with finite volume. From this point of view, we reexamine the primordial non-Gaussianity in single field models, focusing on the bispectrum in the squeezed limit. A conventional prediction states that the bispectrum in this limit is related to the power spectrum through the so-called consistency relation. However, it turns out that, if we adopt a genuine gauge invariant variable which is naturally composed purely of the information in our local universe, the leading term for the bispectrum in the squeezed limit predicted by the consistency relation vanishes.