Large-scale cosmological structure and topologically stable states of a scalar field which are periodic in the radial coordinate.

Mathematics – Logic

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Cosmological Models: Friedmann Universe, Cosmological Models: Galaxy Distribution

Scientific paper

A quasistatic stable state of a scalar field in a closed Friedmann universe with a periodic distribution of energy density along the radial coordinate is described. The classical solution is stable by virtue of the angular nature of the pseudo-Goldstone scalar field (the self-effect of this field is described by a cosinusoidal potential). As a result, there is a conserved topological number (the winding number). The solution found here is linked with a possible periodicity in the distribution of galaxies [T. J. Broadhurst et al., Nature, Vol. 343, p. 726 (1990)]. Physically, it appears that this may not be a complete solution, applying over the entire closed universe. It may instead be only a linear metastable fragment of this entire solution, which decays because of smearing at the ends after a sufficiently long time.

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