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

In order to estimate the effects of a local structure on the Hubble parameter we calculate the low-redshift expansion for H ( z ) and δ H H for an observer at the center of a spherically symmetric matter distribution in the presence of a cosmological constant. We then test the accuracy of the formulas comparing them with fully relativistic non-perturbative numerical calculations for different cases for the density profile. The low-redshift expansion we obtain gives results more precise than perturbation theory since it is based on the use of an exact solution of Einstein’s field equations. For larger density contrasts the low-redshift formulas 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 an assumption. The formulas 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 Λ C D M prediction compatible with the formulas we have derived, this could be considered an independent evidence of the existence of a local inhomogeneity, and the formulas could be used to determine the characteristics of this local structure.