# A possible solution to the Hubble constant discrepancy -- Cosmology where the local volume expansion is driven by the domain average density

## TL;DR

This paper proposes that the Hubble constant discrepancy can be explained by inhomogeneities in the universe, using linear perturbation theory and spatial averaging within general relativity, without invoking exotic matter or non-linear effects.

## Contribution

It introduces a novel explanation for the Hubble constant discrepancy based on first-order inhomogeneities and spatial averaging in a general relativistic framework, avoiding complex non-linear models.

## Key findings

- The Hubble constant discrepancy can be addressed with linear perturbation effects.
- Spatial averaging over finite domains influences local expansion measurements.
- No exotic matter or non-linear effects are necessary for this explanation.

## Abstract

The Hubble constant problem is the discrepancy between different measurements of the Hubble constant in different scales. We show that this problem can be resolved within the general relativistic framework of the perturbation theory in the inhomogeneous universe, with the help of spatial averaging procedure over a finite local domain in the $t=\mbox{const.}$ hypersurface. The idea presented in this paper is unique in the sense that it has all of the following properties. a) It is based on the general relativistic perturbation theory, with ordinary dust matter only. No strange matter nor energy components are required. b) The employment of the spatially invariant averaging procedure on the finite domain is essential. c) The key is the first-order effect of the inhomogeneities in the linear perturbation theory. No non-linear effects are required.