A CFT interpretation of cosmological correlation functions in $\alpha-$vacua in de-Sitter space

TL;DR

This paper presents a method to compute cosmological correlation functions in $\alpha$-vacua of de-Sitter space, relating them to 3D CFT correlators and relaxing OPE consistency in momentum space.

Contribution

It introduces a simple prescription to derive $\alpha$-vacua correlation functions from Bunch-Davies vacuum and connects them to 3D CFTs by relaxing OPE constraints.

Findings

Correlation functions in $\alpha$-vacua can be computed from BD vacuum.

Relaxing OPE consistency relates $\alpha$-vacua correlators to 3D CFTs.

Method simplifies analysis of $\alpha$-vacua in de-Sitter space.

Abstract

de-Sitter(dS) space allows for a generalized class of vacua, known as $\alpha-$vacua, described by some parameters. The Bunch-Davies (BD) vacua is a point in this parameter space. The cosmological correlation function is mostly discussed in BD vacuum in four dimensions and can be interpreted as $CFT_3$ correlation function of certain operators. However, the correlation function in $\alpha-$vacua takes a much more complicated form. In this paper, we give a simple prescription to compute correlation function in $\alpha-$vacua in terms of correlation function of BD vacuum. We also show that the correlation function in the $\alpha-$vacua can be related to three-dimensional CFT correlation functions if we relax the requirement of consistency with OPE limit. Relaxation of consistency with OPE limit can be naturally achieved in momentum space.