Cosmological Geometric Phase From Pure Quantum States: A study without/with having Bell's inequality violation

TL;DR

This paper derives the cosmological geometric phase from quantum states during the early universe, analyzing effects with and without Bell's inequality violation, and connects theoretical results with cosmological observations.

Contribution

It provides analytical expressions for the cosmological geometric phase considering Bell's inequality violation in different regimes, linking quantum features to observable cosmological parameters.

Findings

Derived explicit formulas for the geometric phase in various regimes.

Connected quantum geometric phase with spectral index and tensor-to-scalar ratio.

Provided numerical constraints on the geometric phase consistent with observations.

Abstract

In this paper, using the concept of Lewis Riesenfeld invariant quantum operator method for finding continuous eigenvalues of quantum mechanical wave functions we derive the analytical expressions for the cosmological geometric phase, which is commonly identified to be the Pancharatnam Berry phase from primordial cosmological perturbation scenario. We compute this cosmological geometric phase from two possible physical situations,(1) In the absence of Bell's inequality violation and (2) In the presence of Bell's inequality violation having the contributions in the sub Hubble region ($-k\tau\gg 1$), super Hubble region ($-k\tau\ll 1$) and at the horizon crossing point ($-k\tau= 1$) for massless field ($m/{\cal H}\ll 1$), partially massless field ($m/{\cal H}\sim 1$) and massive/heavy field ($m/{\cal H}\gg 1$), in the background of quantum field theory of spatially flat quasi De Sitter geometry. The prime motivation for this work is to investigate the various unknown quantum mechanical features of primordial universe. To give the realistic interpretation of the derived theoretical results we express everything initially in terms of slowly varying conformal time dependent parameters, and then to connect with cosmological observation we further express the results in terms of cosmological observables, which are spectral index/tilt of scalar mode power spectrum ($n_{\zeta}$) and tensor-to-scalar ratio ($r$). Finally, this identification helps us to provide the stringent numerical constraints on the Pancharatnam Berry phase, which confronts well with recent cosmological observation.