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We pursue a program to confront observations with inhomogeneous extensions of the FLRW metric. The main idea is to test the Copernican principle (CP) rather than assuming it a priori. We consider the ΛCDM model endowed with a spherical ΛLTB inhomogeneity around us, that is, we assume isotropy and test the hypothesis of homogeneity. We confront the ΛLTB model with the latest available data from cosmic microwave background, BAO, type Ia supernovae, local H 0, cosmic chronometers, Compton y-distortion, and kinetic Sunyaev–Zeldovich effect. We find that these data can constrain tightly this extra inhomogeneity, almost to the cosmic variance level: on scales ≳ 100 Mpc structures can have a small non-Copernican effective contrast of just δ L ∼ 0.01. Furthermore, the constraints on the standard ΛCDM parameters are not weakened after marginalizing over the parameters that model the local structure, to which we assign ignorance priors. In other words, dropping the CP assumption does not imply worse constraints on the cosmological parameters. This positive result confirms that the present and future data can be meaningfully analyzed within the framework of inhomogeneous cosmology. [ABSTRACT FROM AUTHOR]

A dark-energy, which behaves as the cosmological constant until a sudden phantom transition at very low redshift (z < 0.1), seems to solve the >4σ disagreement between the local and high-redshift determinations of the Hubble constant, while maintaining the phenomenological success of the Λ cold dark matter model with respect to the other observables. Here, we show that such a hockey-stick dark energy cannot solve the H 0 crisis. The basic reason is that the supernova absolute magnitude MB that is used to derive the local H 0 constraint is not compatible with the MB that is necessary to fit supernova, baryon acoustic oscillation, and cosmic microwave background data, and this disagreement is not solved by a sudden phantom transition at very low redshift. We make use of this example to show why it is preferable to adopt in the statistical analyses the prior on MB as an alternative to the prior on H 0. The three reasons are: (i) one avoids potential double counting of low-redshift supernovae, (ii) one avoids assuming the validity of cosmography, in particular, fixing the deceleration parameter to the standard model value q 0 = −0.55, (iii) one includes in the analysis the fact that MB is constrained by local calibration, an information which would otherwise be neglected in the analysis, biasing both model selection and parameter constraints. We provide the priors on MB relative to the recent Pantheon and DES-SN3YR supernova catalogs. We also provide a Gaussian joint prior on H 0 and q 0 that generalizes the prior on H 0 by Supernova H0 for the Equation of State. [ABSTRACT FROM AUTHOR]