A Proposal for Constraining Initial Vacuum by CMB

TL;DR

This paper introduces a theoretical approach to constrain the initial vacuum state in the early universe using CMB observations, analyzing correlation functions and Bogolyubov coefficients.

Contribution

It presents a novel framework that constrains vacuum parameters directly from CMB data without assuming a specific initial vacuum state.

Findings

Derived relations between Bogolyubov coefficients using observational data

Computed observable parameters from two- and three-point correlation functions

Outlined the advantages and limitations of the proposed method

Abstract

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.