Local observer effect on the cosmological soft theorem

TL;DR

This paper investigates how the local observer effect influences the cosmological soft theorem, particularly the trispectrum and the inequality between non-Gaussianity parameters, ensuring the robustness of these indicators during inflation.

Contribution

It demonstrates that the local observer effect does not alter the fundamental inequality between $f_{NL}$ and $ au_{NL}$, preserving its role as a probe of light degrees of freedom during inflation.

Findings

The trispectrum in the collapsed limit is shifted by the rescaling from soft modes.

The inequality between $f_{NL}$ and $ au_{NL}$ remains unaffected by the local observer effect.

Comments on the local observer effect on the ultra slow-roll inflation consistency relation.

Abstract

Non-Gaussianities of primordial perturbations in the soft limit provide the important information about the light degrees of freedom during inflation. The soft modes of the curvature perturbations, unobservable for a local observer, act as rescaling the spatial coordinates. We determine how the trispectrum in the collapsed limit is shifted by the rescaling due to the soft modes. We find the form of the inequality between $f_{\rm NL}$ and $\tau_{\rm NL}$ parameters is not affected by the rescaling, demonstrating that the role of the inequality as an indicator of the light degrees of freedom remains intact. We also comment on the local observer effect on the consistency relation for ultra slow-roll inflation.