Tension in the void: cosmic rulers strain inhomogeneous cosmologies

New constraints on inhomogeneous Lemaȋtre-Tolman-Bondi (LTB) models alternative to Dark Energy are presented, focusing on adiabatic profiles with space-independent Big Bang and baryon fraction. The Baryon Acoustic Oscillation (BAO) scale at early times is computed in terms of the asymptotic value and then projected to different redshifts by following the geodesics of the background metric. Additionally, a model-independent method to constraint the local expansion rate using a prior on supernovae luminosity is presented. Cosmologies described by an adiabatic GBH matter profile with Ω_out = 1 and Ω_out ⩽ 1 are investigated using a Markov Chain Monte Carlo analysis including the latest BAO data from the WiggleZ collaboration and the local expansion rate from the Hubble Space Telescope, together with Union2 type Ia supernovae data and the position and height of the Cosmic Microwave Background acoustic peaks. The addition of BAO data at higher redshifts increases considerably their constraining power and represents a new drawback for this type of models, yielding a value of the local density parameter Ω_in≳0.2 which is 3σ apart from the value Ω_in≲0.15 found using supernovae. The situation does not improve if the asymptotic flatness assumption is dropped, and a Bayesian analysis shows that constrained GBH models are ruled out at high confidence. We emphasize that these are purely geometric probes, that only recently have become sufficiently constraining to independently rule out the whole class of adiabatic LTB models.