Relativistic Wavepackets in Classically Chaotic Quantum Cosmological Billiards

Abstract

Close to a spacelike singularity, pure gravity and supergravity in four to eleven spacetime dimensions admit a cosmological billiard description based on hyperbolic Kac-Moody groups. We investigate the quantum cosmological billiards of relativistic wavepackets towards the singularity, employing flat and hyperbolic space descriptions for the quantum billiards. We find that the strongly chaotic classical billiard motion of four-dimensional pure gravity corresponds to a spreading wavepacket subject to successive redshifts and tending to zero as the singularity is approached. We discuss the possible implications of these results in the context of singularity resolution and compare them with those of known semiclassical approaches. As an aside, we obtain exact solutions for the one-dimensional relativistic quantum billiards with moving walls.

18 pages, 10 figures

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• On fundamental domains and volumes of hyperbolic Coxeter-Weyl groups
• Reflections on the hyperbolic plane
• Measuring acceleration using the Purcell effect