Aspects of soliton physics: Existence of static solitons in an expanding universe and quantum soliton-antisoliton annihilation

Details Aspects of soliton physics: Existence of static solitons in an expanding universe and quantum soliton-antisoliton annihilation Aspects of soliton physics: Existence of static solitons in an expanding universe and quantum soliton-antisoliton annihilation

Dec 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998phdt.......154p&link_type=abstract

Thesis (PhD). MASSACHUSETTS INSTITUTE OF TECHNOLOGY, Source DAI-B 59/09, p. 4894, Mar 1999, pages.

Computer Science

Scientific paper

We prove that static solitons exist in the 1 + 1 dimensional Sine-Gordon theory in an expanding de Sitter universe if and only if α≡[[m2]/over[H2]] > 2, where m is the mass parameter of the Sine-Gordon theory and H the Hubble constant. The threshold /alpha = 2 is then qualitatively explained in terms of the interplay between the gravitational tidal forces (that tend to pull a soliton apart) and the restoring tensile forces in the soliton (that resist any perturbation of the soliton). In fact, we show that, by comparing the estimates of the tensile force in the soliton and the tidal force of de Sitter spacetime, one can not only infer the existence of a threshold in α but also obtain an estimate of the threshold which agrees with the exact value (α = 2) to within a factor of 4. Using a similar argument, in terms of tidal and restoring forces, we also show that a static 't Hooft-Polyakov monopole (with vanishing Higgs self- coupling) can exist in an expanding universe only if [(gF)2/over H2]/ ~>/ 20, where g is the gauge coupling constant and F, the Higgs vacuum expectation value. These results predict that for a suitable range of parameters, solitons in the early universe inevitably succumb to eternal inflation at their core and do not survive in a simple form subsequently. Next we investigate the important outstanding problem of computing the quantum amplitude of soliton-antisoliton annihilation. We show that, using a given classical solution describing soliton-antisoliton annihilation into mesons, one can construct a quantum scattering process in which an initial quantum state comprising a soliton- antisoliton pair scatters into a final coherent state comprising mesons. By calculating the tree level amplitude of this scattering process, we show that the quantum soliton-antisoliton annihilation amplitude is not exponentially suppressed, in contrast to the amplitude for soliton-antisoliton pair production in a two-meson collision, which is believed to be exponentially suppressed. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

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