Remarks on overestimating the effects of inhomogeneities on the Hubble constant

TL;DR

This paper examines how small-scale inhomogeneities in the universe can significantly bias measurements of the Hubble constant, emphasizing the need for proper modeling of structure formation to resolve the Hubble tension.

Contribution

It demonstrates that improper treatment of inhomogeneities can cause large deviations in Hubble constant estimates, highlighting the importance of accurate structure formation models.

Findings

Inhomogeneities can cause deviations comparable to the Hubble tension.

Adopting the adhesion model helps assess the impact of structure formation.

Proper modeling reduces bias in Hubble constant measurements.

Abstract

The Hubble constant is one of the most important parameters in cosmology. Discrepancies in values of the Hubble constant estimated from various measurements, the so-called Hubble tension, are a serious problem. In this paper, we study the effects of small-scale inhomogeneities of structure formation on the measurement of the Hubble constant using the luminosity distance-redshift relation. By adopting the adhesion model in Newtonian cosmology as the model of structure formation, we investigate whether or not the effects of inhomogeneities can be sufficiently large to affect the current observations of the Hubble constant. We show that inappropriate treatment of the effects of inhomogeneities can cause a large deviation of the measured value of the Hubble constant from the background value, whose magnitude is comparable with the Hubble tension. Our main message is the importance of adopting an appropriate model of structure formation to investigate the effects of inhomogeneities. We also add discussion on the spatial averaging approach used to estimate the measured Hubble constant in the inhomogeneous universe.