Non-Gaussianity of scalar perturbations generated by conformal mechanisms

TL;DR

This paper analyzes the non-Gaussian features of scalar perturbations generated by conformal mechanisms, revealing a universal behavior at non-linear order and characterizing the trispectrum with a distinctive folded limit singularity.

Contribution

It demonstrates the universal non-linear behavior of perturbations in conformal models and provides the first detailed calculation of their intrinsic trispectrum, highlighting unique features.

Findings

Perturbations behave similarly across models at non-linear order.

Intrinsic bispectrum vanishes, trispectrum shows a folded limit singularity.

Non-Gaussianities can be of detectable size.

Abstract

We consider theories which explain the flatness of the power spectrum of scalar perturbations in the Universe by conformal invariance, such as conformal rolling model and Galilean Genesis. We show that to the leading {\it non-linear} order, perturbations in all models from this class behave in one and the same way, at least if the energy density of the relevant fields is small compared to the total energy density (spectator approximation). We then turn to the intrinsic non-Gaussianities in these models (as opposed to non-Gaussianities that may be generated during subsequent evolution). The intrinsic bispectrum vanishes, so we perform the complete calculation of the trispectrum and compare it with the trispecta of local forms in various limits. The most peculiar feature of our trispectrum is a (fairly mild) singularity in the limit where two momenta are equal in absolute value and opposite in direction (folded limit). Generically, the intrinsic non-Gaussianity can be of detectable size.