  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.
