Bogomol'nyi bounds for cosmic strings

We establish Bogomol'nyi inequalities for the deficit angle of some cylindrically symmetric asymptotically local flat (CALF) spacetimes containing cosmic strings. These results prove the stability against arbitrary cylindrical deformations of those configurations which saturate the bound. Such configuration satisfy first order equations which can, in some cases, be solved exactly.     

Fundamental cosmic strings

Cosmic strings are linear concentrations of energy that may be formed at phase transitions in the very early universe. At one time they were thought to provide a possible origin for the density inhomogeneities from which galaxies eventually develop, though this idea has been ruled out, primarily by observations of the cosmic microwave background (CMB). Fundamental strings are the supposed building blocks of all matter in superstring theory or its modern version, M-theory. These two concepts were originally very far apart, but recent developments have brought them closer. The ‘brane-world’ scenario in particular suggests the existence of macroscopic fundamental strings that could well play a role very similar to that of cosmic strings.

In this paper, we outline these new developments, and also analyse recent observational evidence, and prospects for the future.     

Self-gravitating general-relativistic cosmic strings

We examine the coupled Einstem-Euler-Lagrange equations for nonstationary cosmic strings. Self-consistent solutions to all the equations are found under the assumption that the energy-momentum tensor is of the formT _t ^t =T _z ^z while all other components vanish. It is shown that the strings are necessarily static in this case and that the scalar field potential must be of the usual quartic form with the coupling constants satisfying e²=8.     

Stable charged cosmic strings

We study the quantum stabilization of a cosmic string by a heavy fermion doublet in a reduced version of the standard model. We show that charged strings, obtained by populating fermionic bound state levels, become stable if the electroweak bosons are coupled to a fermion that is less than twice as heavy as the top quark. This result suggests that extraordinarily large fermion masses or unrealistic couplings are not required to bind a cosmic string in the standard model. Numerically we find the most favorable string profile to be a simple trough in the Higgs vacuum expectation value of radius ≈10(-18) m. The vacuum remains stable in our model, because neutral strings are not energetically favored.     

Skyrme-Einstein closed cosmic chiral strings

Within the theory of general relativity, the configuration of a closed string (vortex) characterized by a topological charge of the degree type is described for the Skyrme-Einstein SU (2) chiral model. In the approximation of a large vortex-closure radius (a), a solution to equations of motion is obtained, along with estimates for the vortex energy and radius.