Modelling Cosmic Springs with Finsler and Generalised Finsler Geometries

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.