The radial BAO scale and cosmic shear, a new observable for inhomogeneous cosmologies

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As an alternative explanation of the dimming of distant supernovae ithas recently been advocated that we live in a special place in theUniverse near the centre of a large spherical void described by aLemaître-Tolman-Bondi (LTB) metric. In this scenario, the Universe is no longer homogeneous and isotropic, and the apparent late time acceleration is actually a consequence of spatial gradients. We propose in this paper a new observable, the normalized cosmic shear, written in terms of directly observable quantities, and calculable in arbitrary inhomogeneous cosmologies. This will allow future surveys to determine whether we live in a homogeneous universe or not.In this paper we also update our previous observational constraints from geometrical measures of the background cosmology. We include the Union Supernovae data set of 307 Type Ia supernovae, the CMB acousticscale and the first measurement of the radial baryon acoustic oscillationscale. Even though the new data sets are significantly more constraining, LTB models—albeit with slightly larger voids—are still in agreement with observations, at χ2/d.o.f. = 309.1/(310−4) = 1.01.Together with the paper we also publish the updated easyLTB code used for calculating the models and for comparing them to the observations.