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

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 ($m/\mathcal{H}\ll 1$), partially massless field ($m/\mathcal{H}\sim 1$) and massive/heavy field ($m/\mathcal{H}\gg 1$), 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.

arXiv comment60 pages, 20 figures, 1 table, Revised version accepted for publication in Fortschritte der Physik - Progress of Physics

References in corpus (147)

• Berry Phase Effects on Electronic Properties
• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Planck 2018 results. X. Constraints on inflation
• A bound on chaos
• The Effective Field Theory of Inflation
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Single field consistency relation for the 3-point function
• Effective Field Theory for Inflation
• Quasi-Single Field Inflation and Non-Gaussianities
• The Effective Field Theory of Dark Energy
• On graviton non-Gaussianities during inflation
• Non-Gaussianities in Single Field Inflation and their Optimal Limits from the WMAP 5-year Data
• Limits on non-Gaussianities from WMAP data
• Inflation and squeezed quantum states
• On Soft Limits of Inflationary Correlation Functions
• Large non-Gaussianities with Intermediate Shapes from Quasi-Single Field Inflation
• Geometric phase from Aharonov-Bohm to Pancharatnam-Berry and beyond
• Assisted inflation via tachyon condensation
• On non-gaussianities in single-field inflation
• Out-of-time-order correlators in quantum mechanics
• The Effective Field Theory of Multifield Inflation
• Les Houches Lectures on De Sitter Space
• Optimal limits on f_{NL}^{local} from WMAP 5-year data
• Inconsistency in the application of the adiabatic theorem
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Quasi-Single Field Inflation with Large Mass
• The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds
• Entanglement entropy in de Sitter space
• On the role of potentials in the Aharonov-Bohm effect
• Second-order Gauge Invariant Cosmological Perturbation Theory: -- Einstein equations in terms of gauge invariant variables --
• Resilience of the standard predictions for primordial tensor modes
• Lecture notes on interacting quantum fields in de Sitter space
• Limits on f_NL parameters from WMAP 3yr data
• Galilean symmetry in the effective theory of inflation: new shapes of non-Gaussianity
• Productive Interactions: heavy particles and non-Gaussianity
• Signatures of the Quantization of Gravity at Gravitational Wave Detectors
• A model with cosmological Bell inequalities
• Inflationary Perturbations: the Cosmological Schwinger Effect
• Quantum Mechanics of Gravitational Waves
• Estimators for local non-Gaussianities
• Universal scaling in fast quantum quenches in conformal field theories
• Signals of a Quantum Universe
• Obstructions to Bell CMB Experiments
• An accurate bound on tensor-to-scalar ratio and the scale of inflation
• Cosmological Complexity
• Bell violation in the Sky
• Prospects of inflation in delicate D-brane cosmology
• Hybrid Inflation and Brane-Antibrane System
• Low & High scale MSSM inflation, gravitational waves and constraints from Planck
• Universality in fast quantum quenches
• Entanglement entropy of $\alpha$-vacua in de Sitter space
• Entanglement entropy of squeezed vacua on a lattice
• Tensor Squeezed Limits and the Higuchi Bound
• Fourth level MSSM inflation from new flat directions
• DBI Galileon inflation in background SUGRA
• Quantum discord in de Sitter space
• The Supersymmetric Effective Field Theory of Inflation
• Implications of the scalar tilt for the tensor-to-scalar ratio
• Smooth and fast versus instantaneous quenches in quantum field theory
• Out-of-time-order correlator in coupled harmonic oscillators
• Inflation and dark energy arising from geometrical tachyons
• High-Scale Inflation and the Tensor Tilt
• Priomordial non-Gaussian features from DBI Galileon inflation
• Brane inflation in background supergravity
• Bell's Inequalities for Continuous-Variable Systems in Generic Squeezed States
• Canonical transformations and squeezing formalism in cosmology
• Entangled de Sitter from Stringy Axionic Bell pair I: An analysis using Bunch Davies vacuum
• The Rise of Cosmological Complexity: Saturation of Growth and Chaos
• Cosmological perturbation theory
• Inflationary soft theorems revisited: A generalized consistency relation
• Bell violation in primordial cosmology
• Non-minimally Coupled Tachyonic Inflation in Warped String Background
• Quantum entanglement in de Sitter space from Stringy Axion: An analysis using $\alpha$ vacua
• Thermal out-of-time-order correlators, KMS relations, and spectral functions
• Indirect detection of gravitons through quantum entanglement
• Impact of quantum entanglement on spectrum of cosmological fluctuations
• Can Effective Field Theory of inflation generate large tensor-to-scalar ratio within Randall Sundrum single braneworld?
• The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization
• Infinite violation of Bell inequalities in inflation
• Constraining $\mathcal{N}=1$ supergravity inflationary framework with non-minimal Kähler operators
• Non-Gaussianities from Perturbing Recombination
• Collective Symmetry Breaking and Resonant Non-Gaussianity
• Consistency relation for single scalar inflation
• Anomalous Dimensions and Non-Gaussianity
• Entanglement negativity in the multiverse
• Quantum Quench and Scaling of Entanglement Entropy
• Vacuum State of the Dirac Field in de Sitter Space and Entanglement Entropy
• Regularization dependence of the OTOC. Which Lyapunov spectrum is the physical one?
• Open Quantum Entanglement: A study of two atomic system in static patch of de Sitter space
• Higgs inflation from new Kähler potential
• Reconstructing inflationary potential from BICEP2 and running of tensor modes
• Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism
• Cosmological implications of quantum entanglement in the multiverse
• Quantum Quenches in Free Field Theory: Universal Scaling at Any Rate
• CMB from EFT
• Constraining $\mathcal{N}=1$ supergravity inflation with non-minimal Kähler operators using $\delta N$ formalism
• Circuit Complexity as a novel probe of Quantum Entanglement: A study with Black Hole Gas in arbitrary dimensions
• Leggett-Garg Inequalities for Squeezed States
• COSMOS-$e^{\prime }$- soft Higgsotic attractors
• Nonclassical primordial gravitational waves from the initial entangled state
• COSMOS-$e^{\prime }$-GTachyon from String Theory
• Quantum quench in matrix models: Dynamical phase transitions, Selective equilibration and the Generalized Gibbs Ensemble
• Reconstructing inflationary paradigm within Effective Field Theory framework
• Quantum entanglement in de Sitter space with a wall, and the decoherence of bubble universes
• Brane inflation: A field theory approach in background supergravity
• The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions
• Double Soft Limits of Cosmological Correlations
• Quantum Quench and Double Trace Couplings
• Inflation from D3-brane motion in the background of D5-branes
• Quantum quench and thermalization of one-dimensional Fermi gas via phase space hydrodynamics
• Quantum states of a generalized time-dependent inverted harmonic oscillator
• Locality and topology in the molecular Aharonov-Bohm effect
• Gravity and Geometric Phases
• Lectures on Inflation
• Running of the Scalar Spectral Index and Observational Signatures of Inflation
• Cosmological spectrum of two-point correlation function from vacuum fluctuation of Stringy Axion field in De Sitter space: A study of the role of Quantum Entanglement
• The Cosmological OTOC: Formulating new cosmological micro-canonical correlation functions for random chaotic fluctuations in Out-of-Equilibrium Quantum Statistical Field Theory
• An introduction to inflation and cosmological perturbation theory
• Toward an Effective Field Theory Approach to Reheating
• The Squeezed OTOC and Cosmology
• Uhlmann's geometric phase in presence of isotropic decoherence
• A note on initial state entanglement in inflationary cosmology
• Out of Time Ordered Quantum Dissipation
• On the running of the spectral index to all orders: a new model dependent approach to constrain inflationary models
• Spectral Representation of Thermal OTO Correlators
• Boost Breaking in the EFT of Inflation
• Inflation with improved D3-brane potential and the fine tunings associated with the model
• Causality and Primordial Tensor Modes
• Quantum Quench in Non-relativistic Fermionic Field Theory: Harmonic traps and 2d String Theory
• Prospects of inflation with perturbed throat geometry
• Squeezed vacua in loop quantum gravity
• Probing Out-of-Time-Order Correlators
• Relating the curvature of De Sitter Universe to Open Quantum Lamb Shift Spectroscopy
• The Holographic Dual of the Entanglement Wedge Symplectic Form
• Measuring the spectral running from cosmic microwave background and primordial black holes
• Consistency relations in multi-field inflation
• Higher order corrections to Heterotic M-theory inflation
• The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations
• The transition from quantum field theory to one-particle quantum mechanics and a proposed interpretation of Aharonov-Bohm effect
• EFT of Inflation: Reflections on CMB and Forecasts on LSS Surveys
• Islands and Uhlmann phase: Explicit recovery of classical information from evaporating black holes
• The phenomenology of squeezing and its status in non-inflationary theories
• The Berry phase in inflationary cosmology
• Bounds on Tensor wave and Twisted Inflation
• Inconsistencies of the Adiabatic Theorem and the Berry Phase
• Holography from Decoherence and Entanglement
• Time-dependent quantum harmonic oscillator: a continuous route from adiabatic to sudden changes

Cited by in corpus (2)

• Imprints of screened dark energy on nonlocal quantum correlations
• The effect of quantum decoherence on inflationary gravitational waves