Observational cosmology using characteristic numerical relativity: Characteristic formalism on null geodesics

TL;DR

This paper adapts the characteristic formalism of numerical relativity for cosmological observations by replacing the radial coordinate with an affine parameter, enabling stable simulations of past null cones in cosmology.

Contribution

It introduces a new metric based on the Bondi-Sachs formalism with an affine parameter, improving cosmological modeling on null geodesics.

Findings

Numerical scheme remains stable and convergent with the new metric.

Model effectively simulates cosmological past null cone behavior.

Addresses limitations of diameter distance in cosmological applications.

Abstract

The characteristic formalism of numerical relativity is based on a system of coordinates aligned with outgoing null cones. While these coordinates were designed for studying gravitational waves, they can also be easily adapted to model cosmological past null cones (PNCs). Similar to observational coordinates in the observational approach to cosmology, this then provides a model that only makes use of information causally connected to an observer. However, the diameter distance, which is used as a radial coordinate, limits the model's cosmological application to the region prior to the PNC refocussing. This is because after refocussing, the diameter distance ceases to be a unique measure of distance. This paper addresses the problem by introducing a metric based on the Bondi-Sachs metric where the radial coordinate is replaced by an affine parameter. A model is derived from this metric and it is then shown how an existing numerical scheme can be adapted for simulation of cosmological PNC behaviour. Numerical calculations on this model are found to have the same stability and convergence properties as the standard characteristic formalism.