Improving cosmic string network simulations

TL;DR

This paper develops methods to accurately simulate moving cosmic strings on a lattice, addressing artefacts that limit speed and cause deceleration, and introduces an improved discretisation to enhance simulation fidelity.

Contribution

The authors introduce two methods for constructing moving strings on the lattice and implement an improved discretisation to reduce artefacts and increase maximum string speed.

Findings

Lattice artefacts impose an effective maximum speed for moving strings.

Deceleration of strings is approximately exponential in velocity.

Improved discretisation reduces deceleration and doubles the achievable string speed.

Abstract

In real-time lattice simulations of cosmic strings in the Abelian Higgs model, the broken translational invariance introduces lattice artefacts; relativistic strings therefore decelerate and radiate. We introduce two different methods to construct a moving string on the lattice, and study in detail the lattice effects on moving strings. We find that there are two types of lattice artefact: there is an effective maximum speed with which a moving string can be placed on the lattice, and a moving string also slows down, with the deceleration approximately proportional to the exponential of the velocity. To mitigate this, we introduce and study an improved discretisation, based on the tree-level L\"{u}scher-Weisz action, which is found to reduce the deceleration by an order of magnitude, and to increase the string speed limit by an amount equivalent to halving the lattice spacing. The improved algorithm is expected to be very useful for 3D simulations of cosmic strings in the early universe, where one wishes to simulate as large a volume as possible.