Calculating Observables in Inhomogeneous Cosmologies I: General Framework

Abstract

We lay out a general framework for calculating the variation of a set of cosmological observables, down the past null cone of an arbitrarily placed observer, in a given arbitrary inhomogeneous metric. The observables include redshift, proper motions, area distance and redshift-space density. Of particular interest are observables that are zero in the spherically symmetric case, such as proper motions. The algorithm is based on the null geodesic equation and the geodesic deviation equation, and it is tailored to creating a practical numerical implementation. The algorithm provides a method for tracking which light rays connect moving objects to the observer at successive times. Our algorithm is applied to the particular case of the Szekeres metric. A numerical implementation has been created and some results will be presented in a subsequent paper. Future work will explore the range of possibilities.

25 pages, 5 figures

References in corpus (20)

• The trouble with $H_0$
• The Laniakea supercluster of galaxies
• Tension between the power spectrum of density perturbations measured on large and small scales
• Local Voids as the Origin of Large-angle Cosmic Microwave Background Anomalies I
• Clarifying the Hubble constant tension with a Bayesian hierarchical model of the local distance ladder
• Sample variance in the local measurements of the Hubble constant
• VLBI measurement of the secular aberration drift
• Galaxy number counts to second order and their bispectrum
• Insensitivity of The Distance Ladder Hubble Constant Determination to Cepheid Calibration Modeling Choices
• A Comparison of Cosmological Parameters Determined from CMB Temperature Power Spectra from the South Pole Telescope and the Planck Satellite
• Solving the Inverse Problem with Inhomogeneous Universes
• Obtaining the spacetime metric from cosmological observations
• Physical and Geometrical Interpretation of the epsilon <= 0 Szekeres Models
• The Mass of the Cosmos
• Determining the metric of the Cosmos: stability, accuracy, and consistency
• Persistent fluctuations in the distribution of galaxies from the Two degree Field Galaxy Redshift Survey
• Differential Density Statistics of Galaxy Distribution and the Luminosity Function
• Solving the Observer Metric
• Frame Rotation in the Szekeres Spacetimes
• Solving Einstein Field Equations in Observational Coordinates with Cosmological Data Functions: Spherically Symmetric Universes with Cosmological Constant

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• Non-perturbative results for the luminosity and area distances
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