# Consistency of the local Hubble constant with the cosmic microwave background

## TL;DR

This paper investigates the tension between local and cosmic microwave background measurements of the Hubble constant, suggesting local inhomogeneities may explain the discrepancy and proposing a reinterpretation of local measurements.

## Contribution

It identifies local matter density fluctuations as a potential source of Hubble constant discrepancy and reinterprets local measurements considering environmental uncertainties.

## Key findings

- Local inhomogeneities can reach 40% in density fluctuations.
- Discrepant expansion rates suggest residing in an underdense region.
- Results show borderline consistency between local and Planck measurements.

## Abstract

A significant tension has become manifest between the current expansion rate of our Universe measured from the cosmic microwave background by the Planck satellite and from local distance probes, which has prompted for interpretations of that as evidence of new physics. Within conventional cosmology a likely source of this discrepancy is identified here as a matter density fluctuation around the cosmic average of the 40 Mpc environment in which the calibration of Supernovae Type Ia separations with Cepheids and nearby absolute distance anchors is performed. Inhomogeneities on this scale easily reach 40% and more. In that context, the discrepant expansion rates serve as evidence of residing in an underdense region of $\delta_{\rm env}\approx-0.5\pm0.1$. The probability for finding this local expansion rate given the Planck data lies at the 95% confidence level. Likewise, a hypothetical equivalent local data set with mean expansion rate equal to that of Planck, while statistically favoured, would not gain strong preference over the actual data in the respective Bayes factor. These results therefore suggest borderline consistency between the local and Planck measurements of the Hubble constant. Generally accounting for the environmental uncertainty, the local measurement may be reinterpreted as a constraint on the cosmological Hubble constant of $H_0=74.7^{+5.8}_{-4.2}$ km/s/Mpc. The current simplified analysis may be augmented with the employment of the full available data sets, an impact study for the immediate $\lesssim10$ Mpc environment of the distance anchors, more prone to inhomogeneities, as well as expansion rates measured by quasar lensing, gravitational waves, currently limited to the same 40 Mpc region, and local galaxy distributions.