A CFT interpretation of cosmological correlation functions in α−vacua in de-Sitter space

Abstract

De-Sitter(dS) space allows for a generalized class of vacua, known as α–vacua, described by some parameters. The Bunch-Davies (BD) vacuum is a point in this parameter space. The cosmological correlation function in BD vacuum in four dimensions and can be interpreted as CFT 3 correlation function of certain operators. However, the correlation function in α–vacua takes a much more complicated form. In this paper, we give a simple prescription to compute correlation function in α–vacua in terms of correlation function of BD vacuum. We also show that the correlation function in the α–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.