The fitting problem in a lattice Universe

We present a regular cubic lattice solution to Einstein field equations that is exact at second order in a small parameter. We show that this solution is kinematically equivalent to the Friedmann-Lemaitre-Robertson-Walker (FLRW) solution with the same averaged energy density. This allows us to discuss the fitting problem in that framework: are observables along the past lightcone of observers equivalent to those in the analogue FLRW model obtained by smoothing spatially the distribution of matter? We find a criterion on the compacity of the objects that must be satisfied in order for the answer to this question to be positive and given by perturbative arguments. If this criterion is not met, the answer to this question must be addressed fully non perturbatively along the past lightcone, even though the spacetime geometry can be described perturbatively.Prepared for the Proceedings of the conference 'Relativity and Gravitation: 100 years after Einstein in Prague', Prague, 25-29th June 2012

Weak gravitational lensing of finite beams

The standard theory of weak gravitational lensing relies on the infinitesimal light beam approximation. In this context, images are distorted by convergence and shear, the respective sources of which unphysically depend on the resolution of the distribution of matter---the so-called Ricci-Weyl problem. In this letter, we propose a strong-lensing-inspired formalism to describe the lensing of finite beams. We address the Ricci-Weyl problem by showing explicitly that convergence is caused by the matter enclosed by the beam, regardless of its distribution. Furthermore, shear turns out to be systematically enhanced by the finiteness of the beam. This implies, in particular, that the Kaiser-Squires relation between shear and convergence is violated, which could have profound consequences on the interpretation of weak lensing surveys.Comment: 6 pages, 2 figures, v2: matches published version, some typos correcte

The theory of stochastic cosmological lensing

On the scale of the light beams subtended by small sources, e.g. supernovae, matter cannot be accurately described as a fluid, which questions the applicability of standard cosmic lensing to those cases. In this article, we propose a new formalism to deal with small-scale lensing as a diffusion process: the Sachs and Jacobi equations governing the propagation of narrow light beams are treated as Langevin equations. We derive the associated Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical results on the mean and dispersion of the angular distance. This formalism is applied to random Einstein-Straus Swiss-cheese models, allowing us to: (1) show an explicit example of the involved calculations; (2) check the validity of the method against both ray-tracing simulations and direct numerical integrations of the Langevin equation. As a byproduct, we obtain a post-Kantowski-Dyer-Roeder approximation, accounting for the effect of tidal distortions on the angular distance, in excellent agreement with numerical results. Besides, the dispersion of the angular distance is correctly reproduced in some regimes.Comment: 37+13 pages, 8 figures. A few typos corrected. Matches published versio