[Paper Review] Classical branches and entanglement structure in the wavefunction of cosmological fluctuations

Elliot Nelson|arXiv (Cornell University)|Oct 31, 2017

Cosmology and Gravitation Theories101 references3 citations

TL;DR

This paper demonstrates how classical behavior emerges in cosmological fluctuations through the entanglement structure of a quantum wavefunction, driven by cosmological dynamics. Starting from a vacuum state, inflation excites long-wavelength modes that, during a subsequent decelerating phase, redundantly entangle with shorter-wavelength modes via gravitational interactions, generating classical records and selecting a preferred basis without hand-picked subsystems or observables.

ABSTRACT

The emergence of preferred classical variables within a many-body wavefunction is encoded in its entanglement structure in the form of redundant classical information shared between many spatially local subsystems. We show how such structure can be generated via cosmological dynamics from the vacuum state of a massless field, causing the wavefunction to branch into classical field configurations on large scales. An accelerating epoch first excites the vacuum into a superposition of classical fields as well as a highly sensitive bath of squeezed super-horizon modes. During a subsequent decelerating epoch, gravitational interactions allow these modes to collect information about longer-wavelength fluctuations. This information disperses spatially, creating long-range redundant correlations in the wavefunction. The resulting classical observables, preferred basis for decoherence, and system/environment decomposition emerge from the translation invariant wavefunction and Hamiltonian, rather than being fixed by hand. We discuss the role of squeezing, the cosmological horizon scale, and phase information in the wavefunction, as well as aspects of wavefunction branching for continuous variables and in field theories.

Motivation & Objective

• To identify the emergence of classical observables in cosmological fluctuations from first principles using quantum entanglement.
• To eliminate reliance on hand-picked subsystems or preferred bases in the decoherence framework.
• To show how redundant classical information arises naturally from spatial entanglement in a translation-invariant wavefunction.
• To explain how long-wavelength modes collect and disperse information about shorter-wavelength fluctuations during a decelerating epoch.
• To clarify the role of squeezing, phase information, and continuous branching in field-theoretic wavefunctions.

Proposed method

• Uses the Bunch-Davies vacuum as the initial state of a massless scalar field in an expanding universe.
• Applies linear and nonlinear dynamics during inflation to generate a superposition of classical field configurations and squeezed super-horizon modes.
• Introduces cubic gravitational interactions (e.g., $\mathcal{L}_3 \sim 3\epsilon a^3 \zeta_L \dot{\zeta}^2$) to model coupling between long- and short-wavelength modes.
• Analyzes the wavefunction’s evolution in phase space using the Schrödinger and Wigner representations to track information dispersal.
• Models the decoherence process via redundant information copies across spatially separated regions, forming classical records.
• Demonstrates that the preferred basis and system/environment decomposition emerge dynamically from the Hamiltonian and wavefunction structure, not by postulate.

Experimental results

Research questions

• RQ1 How can classical observables emerge from a fundamentally quantum wavefunction without assuming a preferred subsystem?
• RQ2 What role does the cosmological expansion—particularly the transition from inflation to deceleration—play in generating classical correlations?
• RQ3 How do gravitational interactions between long- and short-wavelength modes lead to redundant information copies in the wavefunction?
• RQ4 In what way does squeezing of super-horizon modes facilitate the emergence of classical behavior?
• RQ5 How is phase information in the wavefunction related to the selection of a preferred basis for decoherence?

Key findings

• The wavefunction branches into classical field configurations due to long-range, redundant entanglement generated during the post-inflationary decelerating epoch.
• Gravitational interactions during the decelerating phase allow long-wavelength modes to collect and disperse information about shorter-wavelength fluctuations across space.
• The preferred basis for decoherence and the system/environment decomposition emerge dynamically from the translation-invariant Hamiltonian and wavefunction, not by hand.
• Squeezing of super-horizon modes during inflation creates a highly sensitive environment that enables information transfer to shorter-wavelength modes.
• Phase information in the wavefunction is irreversibly dispersed into spatially separated regions, consistent with quantum Darwinism and objective classicality.
• The cubic interaction term $\mathcal{L}_3 \sim 3\epsilon a^3 \zeta_L \dot{\zeta}^2$ is the dominant mechanism for coupling long- and short-wavelength modes, with derivative-suppressed terms neglected.