A Proposal for Constraining Initial Vacuum by CMB

We propose a theoretical framework that can possibly constrain the initial vacuum by Cosmic Microwave Background (CMB) observations. With a generic vacuum without any particular choice a priori, thereby keeping both the Bogolyubov coefficients in the analysis, we compute observable parameters from two- and three-point correlation functions. We are thus left with constraining four model parameters from the two complex Bogolyubov coefficients. We also demonstrate a method of finding out the constraint relations between the Bogolyubov coefficients using the theoretical normalization condition and observational data of power spectrum and bispectrum from CMB. Finally, we discuss the possible pros and cons of the analysis.