Inhomogeneous cosmological models and $H_0$ observations

TL;DR

This paper demonstrates how LTB inhomogeneous cosmological models can be constructed to match any observed Hubble constant, challenging previous claims and enabling alternative explanations to dark energy.

Contribution

It provides a method to build exact LTB solutions matching arbitrary $H_0$ values, facilitating models without dark energy and analyzing local inhomogeneity effects.

Findings

Constructed solutions align with any $H_0$ value.

Method allows for inhomogeneity profiles without restrictive assumptions.

Applications include structure formation and local inhomogeneity effects on dark energy.

Abstract

We address some recent erroneous claim that $H_0$ observations are difficult to accommodate with LTB cosmological models, showing how to construct solutions in agreement with an arbitrary value of $H_0$ by re-writing the exact solution in terms of dimensionless parameters and functions. This approach can be applied to fully exploit LTB solutions in designing models alternative to dark energy without making any restrictive or implicit assumption about the inhomogeneity profile. The same solution can also be used to study structure formation in the regime in which perturbation theory is not enough and an exact solution of the Einstein's equation is required, or to estimate the effects of a local inhomogeneities on the apparent equation of state of dark energy.