Shock-Wave Refinement of the Friedmann-Robertson-Walker Metric

TL;DR

This paper introduces a mathematical framework for relativistic shock waves in cosmology, modeling the Big Bang as a shock wave and suggesting a mechanism for accelerated expansion without dark energy.

Contribution

It develops a novel approach to match expanding FRW metrics with TOV metrics across shock surfaces, providing a new perspective on cosmic acceleration.

Findings

Shock waves can model the Big Bang as a spherical shock surface.

Self-similar perturbations can cause accelerated expansion without a cosmological constant.

The framework applies both inside and outside the Hubble radius.

Abstract

The mathematics of general relativistic shock waves is introduced and considered in a cosmological context. In particular, an expanding Friedmann-Roberson-Walker metric is matched to a Tolman-Oppenheimer-Volkoff metric across a spherical shock surface. This is the general relativistic analogue of a shock-wave explosion within a static singular isothermal fluid sphere and may be regarded as a model for the Big Bang. These shock waves are constructed both within and beyond the Hubble radius, which corresponds to a universe outside and inside its Schwarzschild radius respectively. Certain self-similar perturbations of the FRW metric lead to an accelerated expansion, even without a cosmological constant, and thus it is conjectured that such a mechanism may account for the anomalous acceleration observed today without recourse to dark energy.