Semilocal String Formation

Julian Borrill, University of California, Berkeley, and Lawrence Berkeley National Laboratory

Research Objectives

To model a possible state of the universe only a hundred billionth of a trillionth of a trillionth of a second (10^-35 second) after the Big Bang.

Computational Approach

Using NERSC's Cray T3E, we were able to perform the first full three-dimensional simulations of semilocal string formation. We used a staggered leapfrog discretization of the quantum field equations on a 256 x 256 x 256 periodic lattice. The illustrations show isosurfaces of the flux energy density measured as a fraction of the theoretical peak value.

Accomplishments

Our simulations have shown that non-topological semilocal defects can be energetically stabilized by the back reaction of their gauge field on their scalar sector. We have also seen that the number density of semilocal strings formed depends on the relative strengths of the gauge to the scalar couplings, , ranging from one-third the number density of topological cosmic strings for = 0.05, to the classical stability analysis prediction of no semilocal string for   1.

Significance

Semilocal strings are "worms" of energy that arise from a complex interaction of quantum matter and force fields during a phase transition, such as the fracturing of a unified force into its constituents in the very early universe.

The strings originate as open segments, with a north magnetic monopole on one end and a south monopole on the other. When two oppositely-oriented ends meet, the monopoles annihilate, forming either a closed loop (if the ends belong to the same string) or a longer segment (if the ends belong to different strings). In the first case, the string loops shrink under their own tension and rapidly disappear. In the second case, however, the strings build up into longer and longer objects, ultimately spanning the universe.

If semilocal strings do persist, then they would be a possible source of the primordial density perturbations needed to seed the formation of the gravitationally bound astronomical objects we observe today--from planets to clusters and superclusters of galaxies. In certain models they would also provide a mechanism for baryogenesis, generating the slight asymmetry between matter and antimatter in the early universe that allows us to exist today.

Publications

Ana Achucarro, Julian Borrill, and Andrew R. Liddle, "The formation rate of semilocal strings," Phys. Rev. Lett. (submitted, 1998).

------, "The formation of non-topological string networks," Physica B (in press, 1998).

Julian Borrill, Ana Achucarro, and Andrew R. Liddle, "The rate of formation of semilocal strings," in Proceedings of PASCOS-98, (World Scientific, 1988).

http://cfpa.berkeley.edu/~borrill/defects/semilocal.html