Solving Einstein Field Equations in Observational Coordinates with Cosmological Data Functions: Spherically Symmetric Universes with Cosmological Constant

Abstract

Extending the approach developed by Araújo and Stoeger [1] and improved in Araújo {\it et al} [2], we have shown how to construct dust-filled $\Lambda \ne 0$ Friedmann-Lema\^ıtre-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 (SS) 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 a FLRW universe -- which is not {\it a priori} obvious. It is also shown how to integrate these exact SS 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 non-flat cases to have data giving the maximum of the observer area (angular-diameter) distance, and the redshift $z_{max}$ at which that occurs. This enables the determination of the vacuum-energy density ${\mu }_{\Lambda }$, which would otherwise remain undetermined.

20 pages

References in corpus (5)

• The Limits on Cosmological Anisotropies and Inhomogeneities from COBE Data
• The Mass of the Cosmos
• Inhomogeneous universes in observational coordinates
• Exact isotropic cosmologies with local fractal number counts
• Perturbed Spherically Symmetric Dust Solution of the Field Equations in Observational Coordinates with Cosmological Data Functions

Cited by in corpus (8)

• Inhomogeneous cosmological models: exact solutions and their applications
• Establishing homogeneity of the universe in the shadow of dark energy
• The Lemaitre Model and the Generalisation of the Cosmic Mass
• Solving the Observer Metric
• Calculating Observables in Inhomogeneous Cosmologies I: General Framework
• Obtaining the Time Evolution for Spherically Symmetric Lemaître-Tolman-Bondi Models Given Data on Our Past Light Cone
• Finding a Spherically Symmetric Cosmology from Observations in Observational Coordinates -- Advantages and Challenges
• Cosmological Observations: Averaging on the Null Cone