The arXiv preprint (i.e., free) version is available
here. It's a lot denser than the Science Daily report, and uses the word 'assumption' much more sparingly. Blessings be for that, because the word 'assumption' in popular science is code for 'darned if I know, but let me guess'. For all the interesting math in the paper, it still explains only a quarter of the observed difference between locally observed galactic recessional velocities and the Cosmic Microwave Background. The key relation in the discussion is Fig. 4, which is a portrait of probabilities instead of quantified physical reality. The authors state, 'We show in Fig. 4 the result for the four cases discussed in Table I: it is evident that one needs a very rare large-scale structure to explain away the offset in the Hubble rates. If this tension is further increased, a cosmology beyond the standard model may prove necessary.' While it is not the place of this theoretical speculation to consider what might actually cause the underdensity, there is fact a well-known local OVERdensity lying just beyond the boundaries the paper set for the study. What, exactly, does the paper say is underdense? A: the regional density of matter. The bounds of that region are z=0.01 to 0.023. That corresponds to roughly 50 and 100 million parsecs, or 163 to 326 million light years. But beyond that by 150 million years—at least in a wedge of the sky centered in Ara-Pavo, is the Shapley Supercluster (the spookily-named 'Great Attractor') at 500 mly out, which itself is but a small section of the Great Wall. If there is a regional underdensity, why isn't it countered by an overdensity in the Ara-Pavo Hubble-constant/CMB ratio that doesn't exist in other parts of the sky? Much as I agree with the authors that SOMEthing is causing the discrepancy, I wish it were cast more in terms of real objects in the real sky rather than mathematical curves in a sea of probabilities.
