Determining the metric of the Cosmos: stability, accuracy, and consistency

Abstract

The ultimate application of Einstein's field equations is to empirically determine the geometry of the Universe from its matter content, rather than simply assuming the Universe can be represented by a homogeneous model on all scales. Choosing an LTB model as the most convenient inhomogeneous model for the early stages of development, a data reduction procedure was recently validated using perfect test data. Here we simulate observational uncertainties and improve the previous numerical scheme to ensure that it will be usable with real data as soon as observational surveys are sufficiently deep and complete. Two regions require special treatment--the origin and the maximum in the areal radius. To minimize numerical errors near the origin, we use an LTB series expansion to provide the initial values for integrating the differential equations. We also use an improved method to match the numerical integration to the series expansion that bridges the region near the maximum in the areal radius. Because the mass enclosed within the maximum obeys a specific relationship, we show that it is possible to correct for a fixed systematic error in either the distance scale or the redshift-space mass density, such that the integrated values are consistent with the data at the maximum.

arXiv commentRevision, 21 pages, 6 figures

References in corpus (12)

• Do we really see a cosmological constant in the supernovae data ?
• Large Scale Inhomogeneity Versus Source Evolution -- Can We Distinguish Them Observationally?
• Formation of a galaxy with a central black hole in the Lemaitre-Tolman model
• Shrinking II -- The Distortion of the Area Distance-Redshift Relation in Inhomogeneous Isotropic Universes
• Obtaining the spacetime metric from cosmological observations
• The Mass of the Cosmos
• Relativistic Cosmology Number Counts and the Luminosity Function
• Inhomogeneous universes in observational coordinates
• Differential Density Statistics of Galaxy Distribution and the Luminosity Function
• Clumps into Voids
• Multicolour Observations, Inhomogeneity & Evolution
• Perturbed Spherically Symmetric Dust Solution of the Field Equations in Observational Coordinates with Cosmological Data Functions

Cited by in corpus (20)

• Inhomogeneous cosmological models: exact solutions and their applications
• Establishing homogeneity of the universe in the shadow of dark energy
• A (giant) void is not mandatory to explain away dark energy with a Lemaitre - Tolman model
• Inhomogeneity effects in Cosmology
• Apparent and average acceleration of the Universe
• Imitating accelerated expansion of the Universe by matter inhomogeneities - corrections of some misunderstandings
• Inhomogeneous cosmology and backreaction: Current status and future prospects
• The Metric of the Cosmos from Luminosity and Age Data
• Accelerating expansion or inhomogeneity? A comparison of the $\Lambda$CDM and Lema\^ıtre - Tolman models
• Solving the Observer Metric
• The effect of pressure gradients on luminosity distance - redshift relations
• What's Inside the Cone? Numerically reconstructing the metric from observations
• Calculating Observables in Inhomogeneous Cosmologies I: General Framework
• Observational cosmology using characteristic numerical relativity
• Observational cosmology using characteristic numerical relativity: Characteristic formalism on null geodesics
• Exact inhomogeneous models and the drift of light rays induced by nonsymmetric flow of the cosmic medium
• Consequences of using a smooth cosmic distance in a lumpy universe: I
• Inverse Construction of the $\Lambda$LTB Model from a Distance-redshift Relation
• Finding a Spherically Symmetric Cosmology from Observations in Observational Coordinates -- Advantages and Challenges
• Reconstructing the metric of the local Universe from number counts observations