Primordial fluctuations in extended Liouville theory

TL;DR

This paper models primordial fluctuations during inflation using an extended Liouville theory in 1+1 dimensions, reproducing key features like the scale-invariant spectrum and Maldacena's consistency relation.

Contribution

It introduces a covariant extension of Liouville theory to study inflationary fluctuations and derives the three-point correlation function within this framework.

Findings

Scale-invariant scalar curvature spectrum demonstrated

Three-point function computed in slow roll approximation

Maldacena's consistency relation recovered

Abstract

Liouville gravity can be used to precisely model features of 3+1 dimensional cosmology in a simplified 1+1d setting. We study primordial fluctuations in a generally covariant extension of Liouville theory, in the context of single field inflation. The scale invariant spectrum of scalar curvature perturbations is exhibited, and their three-point correlation function is computed in the slow roll approximation. We recover Maldacena's consistency relation for the three-point function, which in this context depends on a global shift symmetry of extended Liouville theory.