Perturbed Spherically Symmetric Dust Solution of the Field Equations in Observational Coordinates with Cosmological Data Functions

TL;DR

This paper develops a framework for analyzing perturbed spherically symmetric dust solutions in observational coordinates, using cosmological data to understand deviations from the FLRW model on our past light cone.

Contribution

It extends the observational coordinate approach to perturbed FLRW models, addressing gauge issues and data error propagation in cosmological perturbation analysis.

Findings

Formulation of perturbed spherically symmetric solutions with observational data

Resolution of gauge problems in the context of observational coordinates

Guidance on handling data errors and gaps in cosmological perturbation analysis

Abstract

Using the framework for solving the spherically symmetric field equations in observational coordinates given in Araujo and Stoeger (1999), their formulation and solution in the perturbed FLRW sperically symmetric case with observational data representing galaxy redshifts, number counts and observer area distances, both as functions of redshift on our past light cone, are presented. The importance of the central conditions, those which must hold on our world line C, is emphasized. In detailing the solution for these perturbations, we discuss the gauge problem and its resolution in this context, as well as how errors and gaps in the data are propagated together with the genuine perturbations. This will provide guidance for solving, and interpreting the solutions of the more complicated general perturbation problem with observational data on our past light cone.