Light-Cone Observables and Gauge-Invariance in the Geodesic Light-Cone Formalism

Abstract

The remarkable properties of the geodesic light-cone (GLC) coordinates allow analytic expressions for the light-cone observables, providing a new non-perturbative way for calculating the effects of inhomogeneities in our Universe. However, the gauge-invariance of these expressions in the GLC formalism has not been shown explicitly. Here we provide this missing part of the GLC formalism by proving the gauge-invariance of the GLC expressions for the light-cone observables, such as the observed redshift, the luminosity distance, and the physical area and volume of the observed sources. Our study provides a new insight on the properties of the GLC coordinates and it complements the previous work by the GLC collaboration, leading to a comprehensive description of light propagation in the GLC representation.

25 pages, no figures, published in JCAP

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• Cosmological Information Contents on the Light-Cone
• Observed Angles and Geodesic Light-Cone Coordinates
• Maximum Cosmological Information from Type-Ia Supernova Observations
• A Light-Cone Approach to Higher-Order Cosmological Observables
• Infrared Sensitivity of Cosmological Probes in Horndeski Theory
• The gauge invariant cosmological Jacobi map from weak lensing at leading order
• Cosmic Dipoles from Large-Scale Structure Surveys