Tomaschitz, R. (1997). Topological evolution and cosmic chaos, in: XVth Workshop on Geometrical Methods in Physics (Bialowieza, Poland, July 1-7, 1996, A. Strasburger, S. Twareque Ali, A. Odzijewicz, eds.) Reports on Mathematical Physics 40, 359-365 (1997), DOI: 10.1016/S0034-4877(97)85933-2

 

 

Abstract (ScienceDirect, CDS, SAO/NASA ADS, Zbl 0903.58068)

An account on the origins of cosmic chaos and its physical impact in an open and multiply connected universe is given. A new type of cosmic evolution by topological deformations, unpredicted by Einstein's equations, is pointed out. The chaoticity of the galactic world-lines provides a mechanism to create the galactic equidistribution. Global metrical deformations of the open and multiply connected spacelike slices induce angular fluctuations in the temperature of the microwave background. They cause backscattering of electromagnetic fields and particle creation in quantum fields. The topological microstructure of spacetime provides a mechanism for CP violation by self-interference.

 

 

Zbl 0903.58068
Tomaschitz, Roman
Topological evolution and cosmic chaos
[J] Rep. Math. Phys. 40, No.2, 359-365 (1997). ISSN 0034-4877

MSC 2000:

*58Z05 Appl. of global analysis to physics
83F05 Relativistic cosmology

Keywords: metrical deformations; topological microstructure; CP violation; self-interference; cosmic chaos; multiply connected universe

 

Title:

 

Topological evolution and cosmic chaos

Authors:

 

Tomaschitz, Roman

Affiliation:

 

AA(Indian Institute of Astrophysics, Koramangala, Bangalore 560 034, India)

Publication:

 

Reports on Mathematical Physics, vol. 40, issue 2, pp. 359-365

Publication Date:

 

10/1997

Origin:

 

CROSSREF

Keywords:

 

open Robertson-Walker cosmology, temperature anisotropy, microwave background radiation

DOI:

 

10.1016/S0034-4877(97)85933-2

Bibliographic Code:

 

1997RpMP...40..359T

 

 

Figure 1. The horizon at infinity of the Poincaré half-space H3, the universal covering space of the spacelike 3-sections of the RW cosmology. A spacelike slice (F,Γ) is realized in H3 as a polyhedron F with face-identification. The face-pairing transformations generate a discrete group Γ which gives, if applied to the polyhedron, a tessellation Γ(F) of H3 with polyhedral images. This tessellation induces by continuity also a tiling on the boundary of H3, which is depicted here. The complete tiling of H3 is obtained by placing hemispheres onto the circular arcs. This polyhedral tiling of hyperbolic space H3 is the covering space construction for the RW geometry.

 

Figure 1. The horizon at infinity of the Poincaré half-space H3, the universal covering space of the spacelike 3-sections of the RW cosmology. A spacelike slice (F,Γ) is realized in H3 as a polyhedron F with face-identification. The face-pairing transformations generate a discrete group Γ which gives, if applied to the polyhedron, a tessellation Γ(F) of H3 with polyhedral images. This tessellation induces by continuity also a tiling on the boundary of H3, which is depicted here. The complete tiling of H3 is obtained by placing hemispheres onto the circular arcs. This polyhedral tiling of hyperbolic space H3 is the covering space construction for the RW geometry. The qualitative structure of the fractal limit set Λ(Γ) depends on the topology of the 3-slices, which is in turn determined by the covering group [20,21]. In this example, the 3-space fibers over an open interval, with Riemann surfaces (g = 49) as fibers. The chaotic trajectories have covering trajectories with initial and terminal points in the limit set. If the end points are outside Λ(Γ) but close to it, then the trajectory is regular, but it is shadowed by trapped chaotic trajectories over a long period before leaving the chaotic region. The tiling on the boundary of H3 is the key to determine this chaotic nucleus of the open 3-space [5,11]. full size image

 

 

description: Roman Tomaschitz (1997) Topological evolution and cosmic chaos, Reports on Mathematical Physics 40, 359.

 

Keywords: open Robertson–Walker cosmology, multiply connected 3-space of constant negative curvature, temperature anisotropy of the cosmic microwave background radiation, particle creation by metrical deformations of the hyperbolic spacelike slices, topological backscattering, parity violation by self-interference, topological CP violation, fibered hyperbolic 3-manifolds, compact Riemann surfaces, fractal limit sets of quasi-Fuchsian covering groups, Hausdorff dimension, universal covering projection, polyhedral tessellation of hyperbolic space, Poincaré half-space, chaotic world lines, Bernoulli property, hyperbolic convex hull of a fractal limit set, galactic equidistribution in the chaotic center of the universe, deformation spaces of open hyperbolic 3-manifolds, topology change

 

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