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Quantum Cosmology, Decoherence, and the Emergence of Classical Spacetime

Ali Nayeri

Abstract

We analyze the emergence of classical cosmological spacetimes in quantum cosmology by computing the reduced density matrix for long-wavelength curvature perturbations. Starting from standard Hartle--Hawking and tunneling boundary conditions, we emphasize that semiclassical WKB structure and inflationary squeezing do not by themselves yield classicality. Tracing over unobserved degrees of freedom and using the influence functional formalism, we derive the decoherence functional for superhorizon curvature modes during inflation. For a light massive environmental scalar field in the Bunch--Davies vacuum, we obtain an explicit noise kernel and show how a nonzero mass regulates the infrared behavior. We then evaluate decoherence under horizon-based and EFT-motivated coarse grainings, finding efficient suppression of interference between macroscopically distinct perturbation histories in both cases. The analysis clarifies the distinct roles of boundary conditions (branch amplitudes) and decoherence (classical branch selection) and yields an emergent cosmological arrow of time through environment-induced entanglement.

Quantum Cosmology, Decoherence, and the Emergence of Classical Spacetime

Abstract

We analyze the emergence of classical cosmological spacetimes in quantum cosmology by computing the reduced density matrix for long-wavelength curvature perturbations. Starting from standard Hartle--Hawking and tunneling boundary conditions, we emphasize that semiclassical WKB structure and inflationary squeezing do not by themselves yield classicality. Tracing over unobserved degrees of freedom and using the influence functional formalism, we derive the decoherence functional for superhorizon curvature modes during inflation. For a light massive environmental scalar field in the Bunch--Davies vacuum, we obtain an explicit noise kernel and show how a nonzero mass regulates the infrared behavior. We then evaluate decoherence under horizon-based and EFT-motivated coarse grainings, finding efficient suppression of interference between macroscopically distinct perturbation histories in both cases. The analysis clarifies the distinct roles of boundary conditions (branch amplitudes) and decoherence (classical branch selection) and yields an emergent cosmological arrow of time through environment-induced entanglement.
Paper Structure (16 sections, 27 equations, 1 figure)

This paper contains 16 sections, 27 equations, 1 figure.

Table of Contents

  1. Quantum Cosmology Before Classicality
  2. Hilbert's Sixth Problem and Emergent Classicality
  3. Reduced Density Matrix and Influence Functional
  4. Explicit Noise Kernel for a Light Environment Field
  5. Coarse Graining and Emergent Classical Dynamics
  6. Horizon-Based Coarse Graining
  7. EFT-Based Coarse Graining
  8. Order-of-Magnitude Estimates
  9. Hartle--Hawking and Tunneling Proposals After Decoherence
  10. Semiclassical Branch Structure
  11. Reduced Density Matrix in the Branch Basis
  12. Expanding versus Contracting Histories
  13. Boundary Conditions versus Classicality
  14. Emergent Arrow of Time
  15. Discussion and Outlook
  16. ...and 1 more sections

Figures (1)

  • Figure 1: Schematic roadmap (adapted from standard decoherence frameworks, e.g. influence-functional constructions of the Feynman--Vernon type). Quantum-cosmological boundary conditions define the universal state $\Psi$. Tracing over unobserved degrees of freedom yields a reduced density matrix for long-wavelength perturbations. The influence functional encodes dissipation and noise; the associated decoherence functional suppresses interference between macroscopically distinct histories. Classical stochastic descriptions and an operational arrow of time emerge after coarse graining, with the detailed rate depending only weakly on the coarse-graining prescription.