[논문 리뷰] The Cosmological Arrow of Time from Inflationary Branch Decoherence

Ali Nayeri|arXiv (Cornell University)|2026. 02. 24.

Cosmology and Gravitation Theories인용 수 0

한 줄 요약

논문은 inflation 동안 장파장 curvature perturbations에 대한 명시적 decoherence functional을 unobserved degrees of freedom를 tracing over 하여 도출하고, environment-induced decoherence가 coarse-graining 세부사항과 무관하게 emergent cosmological arrow of time과 classicality를 유발함을 보인다.

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 derive the convolution structure and superhorizon scaling of the noise kernel and show how a nonzero mass softens 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. We further derive the branch-overlap factor $|\mathcal{D}_k(z)|$ explicitly from the Bunch--Davies mode functions in the expanding-versus-contracting branch formalism, obtaining the exact closed form $|\mathcal{D}_k(z)|=[z^2/(z^2+1)]^{1/4}$ (massless limit) and the superhorizon power law $|\mathcal{D}_k(z)|\sim z^ν$ (massive fields). Numerical evaluation shows that the geometric (coupling-independent) branch-decoherence functional crosses unity within $\approx0.5$ e-folds, growing irreversibly thereafter, providing a derived account of why expanding cosmological histories acquire robust classical records while contracting ones do not. The analysis clarifies the distinct roles of boundary-condition amplitudes and environment-induced decoherence and connects the emergent cosmological arrow of time directly to inflationary squeezing.

연구 동기 및 목표

• Motivate Hilbert’s Sixth Problem in the cosmological setting and clarify how classical spacetime emerges from a quantum cosmology framework.
• Develop an explicit reduced density matrix for long-wavelength curvature perturbations by tracing out environmental degrees of freedom.
• Derive and analyze the influence functional and decoherence functional for inflationary perturbations.
• Show how boundary conditions (Hartle–Hawking/tunneling amplitudes) and decoherence play distinct roles in selecting classical histories.
• Demonstrate robustness of decoherence under different coarse-graining schemes (horizon-based and EFT-based).

제안 방법

• Construct the universal quantum state under no-boundary and tunneling boundary conditions and express as a WKB-type expansion into semiclassical branches.
• Define system vs environment by separating long-wavelength curvature perturbations from short-wavelength modes and extra fields.
• Compute the influence functional via Schwinger–Keldysh formalism to obtain the noise kernel N and dissipation kernel D.
• Model the environment with a light scalar field in the Bunch–Davies vacuum and derive an explicit noise kernel N for a cubic interaction with the curvature perturbation.
• Analyze decoherence through the decoherence functional Γ and show how it suppresses interference between macroscopically distinct histories.
• Evaluate decoherence under horizon-based and EFT-motivated coarse-grainings and compare their impact on decoherence rates.

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

실험 결과

연구 질문

• RQ1 How does tracing over unobserved degrees of freedom produce an effectively classical reduced density matrix for inflationary perturbations?
• RQ2 What is the explicit form of the noise kernel for a light environmental field coupling to curvature perturbations, and how does mass regulate infrared behavior?
• RQ3 How do horizon-based and EFT-based coarse-grainings affect the rate and robustness of decoherence in inflation?
• RQ4 Do boundary conditions alone suffice to produce classical spacetime, or is decoherence essential to selecting classical histories?
• RQ5 Can an emergent cosmological arrow of time arise dynamically through environment-induced entanglement?

주요 결과

• Decoherence is efficiently generated by environment-induced entanglement, leading to a reduced density matrix that is approximately diagonal in the branch basis.
• A light scalar environment in the Bunch–Davies vacuum yields an explicit noise kernel; a nonzero mass regulates infrared behavior.
• Under both horizon-based and EFT-based coarse graining, interference between macroscopically distinct curvature perturbation histories is rapidly suppressed.
• Boundary conditions set the amplitudes of semiclassical branches, while decoherence selects which branches become classical.
• Expanding histories are dynamically selected as classical due to greater entanglement with the environment, providing an emergent cosmological arrow of time.
• Decoherence rates scale with e-folds and couplings, typically yielding Γ ≥ 1 within a few to about 10 e-folds for reasonable parameter choices in the EFT-based scheme.