Obtaining the spacetime metric from cosmological observations

The Copernican principle asserts homogeneity on very large scales, however, this scale is still not well defined; and in reality homogeneity is assumed. Recent galaxy redshift surveys have brought in a large amount of cosmological data out to redshift 0.3 or more, that is now available for analysis; and their accuracy has been improved dramatically. With future surveys expected to achieve a high degree of completeness out to redshift exceeding 1, and a dramatic increase in the amount of data harvested, it will soon be practical to have a numerical programme for determining the metric of the universe from standard observations. This project is the beginning of a series of developments on such a numerical implementation. It is sensible to start with a simple case - that of spherical symmetry and a dust equation of state. Using observational data from out post light cone, consisting of galaxy redshifts, apparent luminosities, angular diameters and number densities, together with chosen source evolution functions, viz absolute luminosities, true diameters and masses of sources; and applying the algorithm in 43, a set of Lemaître-Tolman-Bondi (LTB) arbitrary functions can be found. This set will specify the LTB model that reproduces the given observations, and hence provides a metric that describes the geometry of the observed universe. We briefly review the theoretical development of this topic from the fundamental paper by Kristian and Sachs, to the ideal observational cosmology programme by Ellis and Stoeger and others. We also discuss some of the most crucial issues that we are currently facing in the study of observational cosmology, for example, the problem of source evolution and selection effects. We then briefly introduce a few recent galaxy redshift surveys, that are available for analysis, or will be available in the near future, and the data that we may use from them. We also discuss how one can obtain the diameter distance, luminosity distance and number density, the observables that are essential to our project. We introduce the LTB metric, the null cone solution and the notation that we use, and thus relate the LTB model to be observables.