On the convergence of cosmographic expansions in Lemaitre-Tolman-Bondi models

TL;DR

This paper investigates the limitations of cosmographic expansions in Lemaître-Tolman-Bondi models, revealing small convergence radii and significant deviations from standard cosmology near observers, which impacts their application to real data.

Contribution

It provides a detailed analysis of the convergence properties of cosmographic expansions in inhomogeneous LTB models, highlighting their limitations and the influence of shear gradients.

Findings

FLRW expansions are poor near the observer but improve at higher redshifts.

Deviations in effective cosmographic parameters can be several orders of magnitude from ΛCDM values.

The convergence radius of the general cosmographic expansion is small across studied models.

Abstract

We study cosmographic expansions of the luminosity distance for a variety of Lemaitre-Tolman-Bondi models which we specify inspired by local large-scale structures of the universe. We consider cosmographic expansions valid for general spacetimes and compare to the Friedmann-Lemaitre-Robertson-Walker (FLRW) limit of the expansions as well as to its naive isotropic extrapolation to an inhomogeneous universe. The FLRW expansions are often poor near the observer but become better at higher redshifts, where the light rays have reached the FLRW background. In line with this we find that the effective Hubble, deceleration and jerk parameters of the general cosmographic expansion are often very different from the global $\Lambda$CDM values, with deviations up to several orders of magnitude. By comparing with the naive isotropic extrapolation of the FLRW expansion, we assess that these large deviations are mainly due to gradients of the shear. Very close to the observer, the general cosmographic expansion is always best and becomes more precise when more expansion terms are included. However, we find that the convergence radius of the general cosmographic expansion is small for all studied models and observers and the general cosmographic expansion becomes poor for most of the studied observers already before a single LTB structure has been traversed. The small radius of convergence of the general cosmographic expansion has also been indicated by earlier work and may need careful attention before we can safely apply the general cosmographic expansion to real data.