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

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.

13 pages, 3 figures, revtex4

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• Holographic No-Boundary Measure
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• Damped perturbations in the no-boundary state
• Decoherent Histories Quantum Mechanics with One 'Real' Fine-Grained History
• The Big Bang, CPT, and neutrino dark matter
• The no-boundary proposal in biaxial Bianchi IX minisuperspace
• Arrows of time and the beginning of the universe
• Quantum Transitions Between Classical Histories: Bouncing Cosmologies
• Quantum Transitions Through Cosmological Singularities
• Supersymmetric dS/CFT
• Thermodynamics of Shearing Massless Scalar Field Spacetimes is Inconsistent With the Weyl Curvature Hypothesis
• Arrows of Time and Initial and Final Conditions in the Quantum Mechanics of Closed Systems Like the Universe
• The Quantum Mechanical Arrows of Time