Inflation and deformation of conformal field theory

TL;DR

This paper investigates a holographic approach to inflation, proposing that the universe's wave function can be represented by a boundary QFT's partition function, especially when the boundary theory is a small deformation of a CFT.

Contribution

It derives a simple relation between curvature perturbation correlators and boundary operator correlators in holographic inflation without specifying bulk gravity dynamics.

Findings

Derived a relation linking curvature perturbation and boundary operator correlators.

Applied Ward-Takahashi identity to relate boundary correlators in the holographic setup.

Discussed the validity of the Suyama-Yamaguchi inequality in this context.

Abstract

It has recently been suggested that a strongly coupled phase of inflation may be described holographically in terms of a weakly coupled quantum field theory (QFT). Here, we explore the possibility that the wave function of an inflationary universe may be given by the partition function of a boundary QFT. We consider the case when the field theory is a small deformation of a conformal field theory (CFT), by the addition of a relevant operator O, and calculate the primordial spectrum predicted in the corresponding holographic inflation scenario. Using the Ward-Takahashi identity associated with Weyl rescalings, we derive a simple relation between correlators of the curvature perturbation and correlators of the deformation operator O at the boundary. This is done without specifying the bulk theory of gravitation, so that the result would also apply to cases where the bulk dynamics is strongly coupled. We comment on the validity of the Suyama-Yamaguchi inequality, relating the bi-spectrum and tri-spectrum of the curvature perturbation.