Cosmology as Relativistic Particle Mechanics: From Big Crunch to Big Bang

TL;DR

This paper models cosmological evolution as geodesic motion of a relativistic particle in an augmented target space, providing exact solutions and a novel perspective on singularities using the Wheeler-deWitt equation.

Contribution

It introduces a new approach to cosmology by deriving geodesic equations from a relativistic particle action in an augmented target space, offering exact solutions and insights into singularity resolution.

Findings

Exact cosmological solutions in hyperbolic target spaces.

Singularities correspond to particle trajectories crossing the Milne horizon.

Potential resolution of cosmological singularities via Wheeler-deWitt analysis.

Abstract

Cosmology can be viewed as geodesic motion in an appropriate metric on an `augmented' target space; here we obtain these geodesics from an effective relativistic particle action. As an application, we find some exact (flat and curved) cosmologies for models with N scalar fields taking values in a hyperbolic target space for which the augmented target space is a Milne universe. The singularities of these cosmologies correspond to points at which the particle trajectory crosses the Milne horizon, suggesting a novel resolution of them, which we explore via the Wheeler-deWitt equation.