The Cosmological Arrow of Time from Inflationary Branch Decoherence

TL;DR

This paper investigates how classical spacetime and the arrow of time emerge in quantum cosmology during inflation, emphasizing the role of decoherence and environment interactions in establishing classicality.

Contribution

It provides an explicit calculation of decoherence for superhorizon modes during inflation, linking boundary conditions, environment effects, and the inflationary arrow of time.

Findings

Decoherence suppresses interference between different cosmological histories within about 0.5 e-folds.

Derived exact branch-overlap factor for expanding versus contracting branches.

Shows classicality emerges due to environment-induced decoherence during inflation.

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 $|\mathcal{D}_k(z)|\sim z^\nu$ (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.