Arrows of Time in the Bouncing Universes of the No-boundary Quantum State

TL;DR

This paper derives the arrows of time from the no-boundary quantum state in a cosmological model, showing they are linked to fluctuation growth and differ between bouncing and recollapsing universes, with implications for causality.

Contribution

It provides a quantum cosmological explanation for the directionality of time based on fluctuation behavior in bouncing and recollapsing universes.

Findings

Fluctuations are small at the bounce and grow outward in bouncing universes.

Fluctuations are small near singularities and grow through expansion and contraction in recollapsing universes.

The arrow of time aligns with fluctuation growth and has different characteristics in bouncing versus recollapsing models.

Abstract

We derive the arrows of time of our universe that follow from the no-boundary theory of its quantum state (NBWF) in a minisuperspace model. Arrows of time are viewed four-dimensionally as properties of the four-dimensional Lorentzian histories of the universe. Probabilities for these histories are predicted by the NBWF. For histories with a regular `bounce' at a minimum radius we find that fluctuations are small at the bounce and grow in the direction of expansion on either side. For recollapsing classical histories with big bang and big crunch singularities we find that the fluctuations are small near one singularity and grow through the expansion and recontraction to the other singularity. The arrow of time defined by the growth in fluctuations thus points in one direction over the whole of a recollapsing spacetime but is bidirectional in a bouncing spacetime. We argue that the electromagnetic, thermodynamic, and psychological arrows of time are aligned with the fluctuation arrow. The implications of a bidirectional arrow of time for causality are discussed.