The luminosity distance-redshift relation up to second order in the Poisson gauge with anisotropic stress

Abstract

We present the generalization of previously published results, about the perturbed redshift and the luminosity-redshift relation up to second order in perturbation theory, for the case of the Poisson gauge and in the presence of anisotropic stress. The results are therefore valid for general dark energy models and (most) modified gravity models. We use an innovative approach based on the recently proposed "geodesic light-cone" gauge. We then compare our finding with other results, which recently appeared in the literature, for the particular case of vanishing anisotropic stress. Arriving at a common accepted expression for the non-linear and relativistic corrections to the redshift and distance-redshift relation is of fundamental importance in view of future cosmological surveys. Thanks to these surveys the Universe will be further probed with high precision and at very different scales, where non-linear and relativistic effects can play a key role.

15 pages, no figures. Published version including a corrigendum submitted to CQG

References in corpus (4)

• New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
• Beyond the Linear-Order Relativistic Effect in Galaxy Clustering: Second-Order Gauge-Invariant Formalism
• Do stochastic inhomogeneities affect dark-energy precision measurements?
• Vector and Tensor Contributions to the Luminosity Distance

Cited by in corpus (5)

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• On the perturbation of the luminosity distance by peculiar motions
• Lensing in the Geodesic Light-Cone coordinates and its (exact) illustration to an off-center observer in Lemaître-Tolman-Bondi models
• Gauge invariance on the light-cone: curvature perturbations and radiative degrees of freedom
• Applications of Cosmological Perturbation Theory in the Late Universe