Solving Einstein field equations in observational coordinates with cosmological data functions: Spherically symmetric universes with a cosmological constant

Extending the approach developed by Araujo and Stoeger [M. E. Araujo and W. R. Stoeger, Phys. Rev. D 60, 104020 (1999)] and improved in Araujo et al.[M. E. Araujo, S. R. M. M. Roveda, and W. R. Stoeger, Astrophys. J. 560, 7 (2001)], we have shown how to construct dust-filled Λ≠0 Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological models from FLRW cosmological data on our past light cone. Apart from being of interest in its own right--demonstrating how such data fully determines the models--it is also illustrated in the flat case how the more general spherically symmetric Einstein field equations can be integrated in observational coordinates with data fit to FLRW forms arrayed on our past light cone, thus showing how such data determines an FLRW universe--which is not a priori obvious. It is also shown how to integrate these exact sypherically symmetric equations, in cases where the data are not FLRW, and the space-time is not known to be flat. It is essential for both flat and nonflat cases to have data giving the maximum of the observer area (angular-diameter) distance, and the redshift zmax at which that occurs. This enables the determination of the vacuum-energy density μΛ, which would otherwise remain undetermined.