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arXiv:2602.21263

The Cosmological Arrow of Time from Inflationary Branch Decoherence

Ali Nayeri

gr-qcastro-ph.COhep-thquant-phSubmitted Feb 24, 2026• Announced Feb 25, 2026• Revised Mar 18, 2026 (v2)
v1 · Feb 24, 2026v2 · Mar 18, 2026v3 · Jun 10, 2026
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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.

Journal reference
Phys. Rev. D 113, 126030 (2026)
DOI
10.1103/1k1w-c7vd
Comments
12 pages, 3 figures

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