Cosmic strings in a space-time with positive cosmological constant

TL;DR

This paper investigates Abelian cosmic strings in de Sitter space, revealing their smooth extension across horizons, oscillating scalar fields, existence limits tied to the cosmological constant, and the impact on space-time geometry.

Contribution

It provides the first detailed analysis of Abelian strings in a de Sitter background, including new radially excited solutions and their effects on space-time structure.

Findings

Strings extend smoothly across horizons.

Oscillating scalar fields outside the horizon.

Existence limited by a maximum cosmological constant.

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.