Relativistic Wavepackets in Classically Chaotic Quantum Cosmological Billiards

Details Relativistic Wavepackets in Classically Chaotic Quantum Cosmological Billiards Relativistic Wavepackets in Classically Chaotic Quantum Cosmological Billiards

2011-07-29

arxiv.org/abs/1107.6023v2

Phys Rev D 85, 063501 (2012)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, 10 figures

Scientific paper

10.1103/PhysRevD.85.063501

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.

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