Local observer effect on the cosmological soft theorem

Abstract

Non-Gaussianities of primordial perturbations in the soft limit provide important information about the light degrees of freedom during inflation. The soft modes of the curvature perturbations, unobservable for a local observer, act to rescale the spatial coordinates. We determine how the trispectrum in the collapsed limit is shifted by the rescaling due to the soft modes. We find that the form of the inequality between the $f_\mathrm{NL}$ and $\tau_\mathrm{NL}$ 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.