A covariant treatment of cosmic parallax

Abstract

The Gaia satellite will soon probe parallax on cosmological distances. Using the covariant formalism and considering the angle between a pair of sources, we find parallax for both spacelike and timelike separation between observation points. Our analysis includes both intrinsic parallax and parallax due to observer motion. We propose a consistency condition that tests the FRW metric using the parallax distance and the angular diameter distance. This test is purely kinematic and relies only on geometrical optics, it is independent of matter content and its relation to the spacetime geometry. We study perturbations around the FRW model, and find that they should be taken into account when analysing observations to determine the parallax distance.

27 pages, 4 figures. v2: Corrected typos, clarified text, sharpened one argument. v3: Added figures, corrected typos, clarified text. Published version

References in corpus (19)

• Cosmology with Weak Lensing Surveys
• Relativistic cosmology and large-scale structure
• A general test of the Copernican Principle
• The universe seen at different scales
• Accelerated expansion from structure formation
• The Szekeres Swiss Cheese model and the CMB observations
• Sachs-Wolfe at second order: the CMB bispectrum on large angular scales
• Applicability of the linearly perturbed FRW metric and Newtonian cosmology
• Cosmic Parallax: possibility of detecting anisotropic expansion of the universe by very accurate astrometry measurements
• Ricci focusing, shearing, and the expansion rate in an almost homogeneous Universe
• Local and non-local measures of acceleration in cosmology
• Dark energy and decompactification in string gas cosmology
• On the relation between the isotropy of the CMB and the geometry of the universe
• Cosmography: Extracting the Hubble series from the supernova data
• Cosmic Parallax in Ellipsoidal Universe
• Cosmic Parallax as a probe of late time anisotropic expansion
• Fitting oscillating string gas cosmology to supernova data
• A model independent measure of the large scale curvature of the Universe
• Cosmological acceleration from a gas of strings

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