Solving the Observer Metric

TL;DR

This paper discusses the observer metric in cosmology, providing a complete spherically symmetric solution and an algorithm for extracting geometric information from observational data along the past null cone.

Contribution

It presents a complete and correct formulation of the spherically symmetric observer metric and an algorithm for reconstructing the metric from observational data, facilitating numerical cosmological analysis.

Findings

Complete spherically symmetric solution in terms of 4 functions

Algorithm for data-driven metric reconstruction

Framework for evolving the metric between null cones

Abstract

The analysis of modern cosmological data is becoming an increasingly important task as the amount of data multiplies. An important goal is to extract geometric information, i.e. the metric of the cosmos, from observational data. The observer metric is adapted to the reality of observations: information received along the past null cone, and matter flowing along timelike lines. It provides a potentially very good candidate for a developing general numerical data reduction program. As a basis for this, we elucidate the spherically symmetric solution, for which there is to date single presentation that is complete and correct. With future numerical implementation in mind, we give a clear presentation of the mathematical solution in terms of 4 arbitrary functions, the solution algorithm given observational data on the past null cone, and we argue that the evolution from one null cone to the next necessarily involves integrating down each null cone.