Geodesic-light-cone coordinates and the Bianchi I spacetime

Abstract

The geodesic-light-cone (GLC) coordinates are a useful tool to analyse light propagation and observations in cosmological models. In this article, we propose a detailed, pedagogical, and rigorous introduction to this coordinate system, explore its gauge degrees of freedom, and emphasize its interest when geometric optics is at stake. We then apply the GLC formalism to the homogeneous and anisotropic Bianchi I cosmology. More than a simple illustration, this application (i) allows us to show that the Weinberg conjecture according to which gravitational lensing does not affect the proper area of constant-redshift surfaces is significantly violated in a globally anisotropic universe; and (ii) offers a glimpse into new ways to constrain cosmic isotropy from the Hubble diagram.

27 pages, 5 figures, v2 matches published version

References in corpus (18)

• Lemaitre-Tolman-Bondi model and accelerating expansion
• How isotropic is the Universe?
• Anisotropic Dark Energy: Dynamics of Background and Perturbations
• Looking the void in the eyes - the kSZ effect in LTB models
• Constraining Dark Energy Anisotropic Stress
• Galaxy number counts to second order and their bispectrum
• Do stochastic inhomogeneities affect dark-energy precision measurements?
• Bianchi Model CMB Polarization and its Implications for CMB Anomalies
• Probing Dark Energy Anisotropy
• Backreaction on the luminosity-redshift relation from gauge invariant light-cone averaging
• The luminosity distance-redshift relation up to second order in the Poisson gauge with anisotropic stress
• Light propagation in a homogeneous and anisotropic universe
• Bianchi I meets the Hubble diagram
• Light propagation in inhomogeneous and anisotropic cosmologies
• Late time anisotropy as an imprint of cosmological backreaction
• Lensing in the Geodesic Light-Cone coordinates and its (exact) illustration to an off-center observer in Lemaître-Tolman-Bondi models
• A framework for testing isotropy with the cosmic microwave background
• Time of flight of ultra-relativistic particles in a realistic Universe: a viable tool for fundamental physics?

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