Obtaining the Time Evolution for Spherically Symmetric Lemaître-Tolman-Bondi Models Given Data on Our Past Light Cone

Abstract

A rigorous demonstration that given appropriate data on our past light cone leads to the determination of the metric functions and all their time derivatives on our past light cone is presented, thus showing how to evolve the solution we obtain from data on the light cone off it in a well-defined and straightforward way. It also automatically gives a procedure for constructing the solution for all spherically symmetric, inhomogeneous cosmological Lemaître-Tolman-Bondi models in observational coordinates as a Taylor series in time of however many terms we need. Our procedure takes into account the essential 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.

21 pages

References in corpus (4)

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• Solving the Observer Metric
• The Angular-Diameter-Distance-Maximum and Its Redshift as Constraints on $\Lambda \ne 0$ FLRW Models
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Cited by in corpus (8)

• Inhomogeneous cosmological models: exact solutions and their applications
• Establishing homogeneity of the universe in the shadow of dark energy
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• Using Time Drift of Cosmological Redshifts to find the Mass-Energy Density of the Universe
• Observational cosmology using characteristic numerical relativity
• Observational cosmology using characteristic numerical relativity: Characteristic formalism on null geodesics
• Towards the geometry of the universe from data
• Finding a Spherically Symmetric Cosmology from Observations in Observational Coordinates -- Advantages and Challenges