Context. Backreactions from large-scale inhomogeneities may provide an elegant explanation for the observed accelerated expansion of the universe without the need to introduce dark energy. Aims. We propose a cosmological test for a specific model of inhomogeneous cosmology, called timescape cosmology. Using large-scale galaxy surveys such as SDSS and 2MRS, we test the variation of expansion expected in the $Lambda$-CDM model versus a more generic differential expansion using our own calibrations of bounds suggested by timescape cosmology. Method. Our test measures the systematic variations of the Hubble flow towards distant galaxies groups as a function of the matter distribution in the lines of sight to those galaxy groups. We compare the observed systematic variation of the Hubble flow to mock catalogues from the Millennium Simulation in the case of the $Lambda$-CDM model, and a deformed version of the same simulation that exhibits more pronounced differential expansion. Results. We perform a series of statistical tests, ranging from linear regressions to Kolmogorov-Smirnov tests, on the obtained data. They consistently yield results preferring $Lambda$-CDM cosmology over our approximated model of timescape cosmology. Conclusions. Our analysis of observational data shows no evidence that the variation of expansion differs from that of the standard $Lambda$-CDM model.
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