Toward verification of large-scale homogeneity in cosmology

Motivated by the desirability of direct observational verification of the large-scale homogeneity of the universe, and relying on assumptions deemed to be well supported by the existing observational data, we develop local models with radial inhomogeneities as a first step toward a detailed framework for comparison with observations. Various observational quantitites are expanded in powers of the redshift. While the leading terms generally coincide with the corresponding Friedmann-Robertson-Walker quantitites, the higher order contributions are modified by the presence of inhomogeneities. It is concluded that inasmuch as the next-to-leading terms (such as the decleration parameter) in such an expansion are generally poorly determined by present observations, the inhomogeneous models developed here are locally indistinguishable from the standard homogeneous models. A possible exception may be the measurement of redshift evolution, should this become feasible with sufficient accuracy