Tomaschitz, R. (1994). Dispersion, topological scattering, and self-interference in multiply connected Robertson-Walker cosmologies, International Journal of Theoretical Physics 33, 353-377, DOI: 10.1007/BF00844977
Abstract (SpringerLink, CDS, SAO/NASA ADS, Zbl 0816.53072)
We investigate scattering effects in open Robertson-Walker cosmologies whose spacelike slices are multiply connected hyperbolic manifolds. We work out an example in which the 3-space is infinite and has the topology of a solid torus. The world-lines in these cosmologies are unstable, and classical probability densities evolving under the horospherical geodesic flow show dispersion, as do the densities of scalar wave packets. The rate of dispersion depends crucially on the expansion factor, and we calculate the time evolution of their widths. We find that the cosmic expansion can confine dispersion: The diameter of the domain of chaoticity in the 3-manifold provides the natural, time-dependent length unit in an infinite, multiply connected universe. In a toroidal 3-space manifold this diameter is just the length of the limit cycle. On this scale we find that the densities take a finite limit width in the late stage of the expansion. In the early stage classical densities and conformally coupled fields approach likewise a finite width; nonconformally coupled fields disperse. Self-interference occurs if the dispersion on the above scale is sufficiently large, so that the wave packet can overlap with itself. Signals can be backscattered through the topology of 3-space, and we calculate their recurrence times.
Zbl
0816.53072
Tomaschitz, Roman
Dispersion, topological scattering, and self-interference in multiply connected
Robertson-Walker cosmologies
[J] Int.
J. Theor. Phys. 33, No.2, 353-377 (1994). ISSN 0020-7748; ISSN
1572-9575
MSC 2000:
*53Z05
Appl. of differential geometry to physics
81Q05 Closed and approximate solutions to quantum-mechanical equations
83F05 Relativistic cosmology
Keywords: Robertson-Walker cosmologies; Gaussian densities; topological scattering; horospherical flows; Klein-Gordon equation; CPT-symmetry
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Dispersion, topological scattering, and self-interference in multiply connected Robertson-Walker cosmologies |
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Tomaschitz, Roman |
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AA(Theoretical Physics Group, Tata Institute of Fundamental Research; Physics Department, University of the Witwatersrand) |
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International Journal of Theoretical Physics, Volume 33, Issue 2, pp.353-377 |
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02/1994 |
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description: Roman Tomaschitz (1994) Dispersion, topological scattering, and self-interference in multiply connected Robertson-Walker cosmologies, International Journal of Theoretical Physics 33, 353.
Keywords: open Robertson–Walker universe, toroidal hyperbolic 3-space, constant negative curvature, hyperbolic solid torus, abelian covering group, Poincaré half-space, universal covering space, unstable world lines, horospherical geodesic flow, covering projection, limit cycle, recurrence times, dispersion of classical and quantum probability densities, classical and quantum currents on open hyperbolic 3-manifolds, global metrical deformations of an open solid torus, semiclassical approximation, horospherical elementary waves, topological backscattering, topological self-interference, wave fields conformally coupled to the background metric, Poincaré series, Eisenstein series
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