  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.
