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

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.