Low red-shift effects of local structure on the Hubble parameter in presence of a cosmological constant

TL;DR

This paper derives precise low-redshift formulas to quantify how local matter structures influence the Hubble parameter, improving upon perturbation theory and aiding in understanding local inhomogeneities in cosmology.

Contribution

It introduces exact low-redshift expansion formulas for $H(z)$ and $rac{ ext{delta} H}{H}$ in a spherically symmetric matter distribution with a cosmological constant, surpassing perturbation theory accuracy.

Findings

Formulas are more precise than perturbation theory for larger density contrasts.

The low-redshift expansion accurately accounts for local structure effects on $H(z)$.

Potential to identify local inhomogeneities through deviations in $H(z)$ observations.

Abstract

In order to estimate the effects of local structure on the Hubble parameter we calculate the low-redshift expansion for $H(z)$ and $\frac{\delta H}{H}$ for an observer at the center of a spherically symmetric matter distribution in presence of a cosmological constant. We then test the accuracy of the formulae comparing them with fully relativistic non perturbative numerical calculations for different cases for the density profile. The low red-shift expansion we obtain gives results more precise than perturbation theory since is based on the use of an exact solution of Einstein's field equations. For larger density contrasts the low red-shift formulae accuracy improves respect to the perturbation theory accuracy because the latter is based on the assumption of a small density contrast, while the former does not rely on such assumption. The formulae can be used to take into account the effects on the Hubble expansion parameter due to the monopole component of the local structure. If the $H(z)$ observations will show deviations from the $\Lambda CDM$ prediction compatible with the formulae we have derived, this could be considered an independent evidence of the existence of a local inhomogeneity, and the formulae could be used to determine the characteristics of this local structure.