Observational cosmology. IV. Perturbed spherically symmetric dust solutions

Abstract

For pt.III see ibid., vol.9, p.509, (1992). The formulation and solution of the perturbed FLRW spherically symmetric field equations for dust are presented with observational data given on a past light cone. Observational coordinates are used. This follows from the treatment of the exact spherically symmetric observational solutions given in Stoeger et al (1992)-and is a preparation for formulating and solving the general FLRW perturbation equations in part V (ibid., vol.9, p.1725 (1992)). The authors explicitly write down both the first and second-order solutions to the perturbed field equations in terms of two unknown data functions r0+(z) and M0+(z), which represent the non-FLRW parts of the observer area distance-redshift and the mass-energy density-redshift relationships, respectively. These two functions are, in practice, given by fitting data sets by some functional form. Constructing concrete solutions using this scheme requires such functions-either presupposed or determined by actual data. Finally, on the basis of these perturbed solutions, a criterion for 'almost FLRW' observational spacetimes is proposed, and other issues, such as that of errors and gaps in the data and their evolution, are discussed.