Sergio Andres Vallejo

arXiv2017

Reconstructing the metric of the local Universe from number counts observations

Number counts observations available with new surveys such as the Euclid mission will be an important source of information about the metric of the Universe. We compute the low red-shift expansion for the energy density and the density contrast using an exact spherically symmetric solution in presence of a cosmological constant. At low red-shift the expansion is more precise than linear perturbation theory prediction. We then use the local expansion to reconstruct the metric from the monopole of the density contrast. We test the inversion method using numerical calculations and find a good agreement within the regime of validity of the red-shift expansion. The method could be applied to observational data to reconstruct the metric of the local Universe with a level of precision higher than the one achievable using perturbation theory.

astro-ph.CO↗

arXiv2016

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

In order to estimate the effects of local structure on the Hubble parameter we calculate the low-redshift expansion for $H(z)$ and $\frac{δH}{H}$ 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 $ΛCDM$ 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.

gr-qc↗