Abstract
We study Abelian strings in a fixed de Sitter background. We find that the gauge and Higgs fields extend smoothly across the cosmological horizon and that the string solutions have oscillating scalar fields outside the cosmological horizon for all currently accepted values of the cosmological constant. If the gauge to Higgs boson mass ratio is small enough, the gauge field function has a power-like behaviour, while it is oscillating outside the cosmological horizon if Higgs and gauge boson mass are comparable. Moreover, we observe that Abelian strings exist only up to a maximal value of the cosmological constant and that two branches of solutions exist that meet at this maximal value. We also construct radially excited solutions that only exist for non-vanishing values of the cosmological constant and are thus a novel feature as compared to flat space–time. Considering the effect of the de Sitter string on the space–time, we observe that the deficit angle increases with increasing cosmological constant. Lensed objects would thus be separated by a larger angle as compared to asymptotically flat space–time.
Highlights
Topological defects are believed to have formed during the phase transitions in the early universe
We found that next to the natural deformations of the standard Abelian Higgs strings, there exist solutions for which the Higgs field function vanishes at some intermediate value of the radial coordinate between the origin and the cosmological horizon
We have studied Abelian Higgs strings in a fixed de Sitter background
Summary
Topological defects are believed to have formed during the phase transitions in the early universe. In [14], a model describing Abelian strings coupled minimally to gravity including a positive cosmological constant have been studied While this model describes the interaction of the matter fields with the gravitational fields properly, the space-time was assumed to have the same symmetries as the string, namely, it was assumed to be cylindrically symmetric. The space-time describing our universe with positive cosmological constant is genuinely spherically symmetric for an inertial observer It is e.g. not difficult to study spherically symmetric topological defects such as magnetic monopoles in a spherically symmetric de Sitter space [16], while it becomes more difficult if one tries to study objects with symmetry different from spherical symmetry.
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