Can the cosmological constant be mimicked by smooth large-scale inhomogeneities for more than one observable?

TL;DR

This paper investigates whether smooth large-scale inhomogeneities can mimic the effects of a cosmological constant across multiple observables, concluding they cannot fit observations as well as the standard Lambda-CDM model.

Contribution

It demonstrates that smooth LTB inhomogeneous models cannot replicate key observational signatures of Lambda-CDM, challenging their viability as dark energy alternatives.

Findings

Smooth LTB models cannot fit luminosity distance and mass density observations simultaneously.

Such models cannot produce a negative apparent deceleration parameter.

Differences in space-time geometry prevent inversion from multiple observables.

Abstract

As an alternative to dark energy it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB) solution of Einstein's field equations. In order to test such an hypothesis we calculate the low redshift expansion of the luminosity distance $D_L(z)$ and the redshift spherical shell mass density $mn(z)$ for a central observer in a LTB space without cosmological constant and show how they cannot fit the observations implied by a $\Lambda CDM $ model if the conditions to avoid a weak central singularity are imposed, i.e. if the matter distribution is smooth everywhere. Our conclusions are valid for any value of the cosmological constant, not only for $\Omega_{\Lambda}>1/3$ as implied by previous proofs that $q^{app}_0$ has to be positive in a smooth LTB space, based on considering only the luminosity distance. The observational signatures of smooth LTB matter dominated models are fundamentally different from the ones of $\Lambda CDM $ models not only because it is not possible to reproduce a negative apparent central deceleration $q^{app}_0$, but because of deeper differences in their space-time geometry which make impossible the inversion problem when more than one observable is considered, and emerge at any redshift, not only for $z=0$.