Understanding the Dyer-Roeder approximation as a consequence of local cancellations of projected shear and expansion rate fluctuations

Abstract

It is shown with several concrete examples that the Dyer-Roeder approximation is valid in spacetimes which fulfill the condition that fluctuations in the expansion rate along a light ray locally cancels with the shear contribution to the redshift. This is the case for standard cosmological scenarios including perturbed FLRW spacetimes, N-body simulations and Swiss-cheese models. With another concrete example it is then illustrated that it is possible to construct statistically homogeneous and effectively statistically isotropic cosmological models which do not fulfill the condition. In this case, the Dyer-Roeder approximation is invalid. Instead, the mean redshift-distance relation can be described using a relation based on the spatial averages of the transparent part of the spacetime.

15 pages, 11 captioned figures. Accepted for publication in PRD

References in corpus (15)

• Inhomogeneous Cosmology with Numerical Relativity
• Another look at redshift drift and the backreaction conjecture
• Ricci focusing, shearing, and the expansion rate in an almost homogeneous Universe
• Integrated Sachs Wolfe Effect and Rees Sciama Effect
• General relativistic weak-field limit and Newtonian N-body simulations
• LTB solutions in Newtonian gauge: from strong to weak fields
• Volume averaging in the quasispherical Szekeres model
• Cosmological nonlinear structure formation in full general relativity
• Constraining the dark energy and smoothness-parameter with supernovae
• Fully relativistic nonlinear cosmological evolution in spherical symmetry using the BSSN formalism
• A New Type of Exact Arbitrarily Inhomogeneous Cosmology: Evolution of Deceleration in the Flat Homogeneous-On-Average Case
• Observational constraints from SNe Ia and Gamma-Ray Bursts on a clumpy universe
• Perturbed redshifts from N-body simulations
• Unbiased constraints on the clumpiness of universe from standard candles
• ZKDR Distance, Angular Size and Phantom Cosmology

Cited by in corpus (2)

• Quantifying effects of inhomogeneities and curvature on gravitational wave standard siren measurements of $H(z)$
• Redshift drift in a universe with structure II: Light rays propagated through a Newtonian N-body simulation