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