Modelling Cosmic Springs with Finsler and Generalised Finsler Geometries

TL;DR

This paper develops a unified geometric framework using Finsler and generalized Finsler geometries to model the dynamics of cosmic strings and springs, revealing conditions for their observational indistinguishability and providing insights into their internal structure.

Contribution

It introduces a novel approach employing Finsler geometries to describe string dynamics without dimensional reduction, unifying various physical phenomena in cosmology.

Findings

Dispersion relations depend on string velocity and curvature.

Unified framework for internal structure of strings and defects.

Conditions for observational indistinguishability of strings and defects.

Abstract

We show that the equations of motion governing the dynamics of strings in a compact internal space can be written as dispersion relations, with a local speed that depends on the velocity and curvature of the string in the large dimensions. From a $(3+1)$-dimensional perspective these can be viewed as dispersion relations for waves propagating in the string interior and are analogous to those for current-carrying topological defects. This allows us to construct a unified framework with which to study and interpret the internal structure of various field-theoretic and fundamental string species, in a simple physically intuitive coordinate system, without the need for dimensional reduction or approximate effective actions. This, in turn, allows us to identify the precise conditions under which higher-dimensional strings and current-carrying defects are observationally indistinguishable, for macroscopic observers. Our approach naturally incorporates the description of so-called `cosmic springs', whose dynamics are expressed in terms of an effective Finsler geometry, for circular loops, or generalised Finsler geometry, for non-circular configurations. This demonstrates the importance of these novel geometric structures and their utility in modelling complex physical phenomena in cosmology and astrophysics.