The redshift dependence of the inferred H₀ in a local void solution to the Hubble tension

Galaxy number counts suggest that we are located within the Gpc-scale KBC void. The Hubble tension might arise due to gravitationally driven outflow from this void, as explored in detail by Haslbauer et al. We explore how the impact of the void on redshift decays at large distances. We define H₀ (z) as the present expansion rate H0 that would be inferred from observations in a narrow redshift range centred on z. We find H₀ (z) in three different ways, all of which give similar results. We then compare these results with the observations of Jia et al., who were careful to minimize the impact of correlations between H₀ measurements from data in different redshift bins. We find reasonable agreement with their results for the Gaussian and exponential void underdensity profiles, although the agreement is less good in the Maxwell–Boltzmann case. The latter profile causes severe disagreement with the observed bulk flow curve at z < 0.1 (Mazurenko et al.), so the tension with higher redshift data further highlights that the deepest part of the KBC void is probably near its centre. The observations show a decline of H₀ (z) towards the background Planck value in qualitative agreement with the considered models, even if we use a larger void. The good overall agreement with the recent results of Jia et al. suggests that the local supervoid evident from the galaxy luminosity density out to a Gpc might also solve the Hubble tension while retaining a low background H₀ consistent with Planck data, assuming enhanced structure formation on > 100 Mpc scales.