Hubble tension and matter inhomogeneities: a theoretical perspective
  We have studied how local density perturbations could reconcile the Hubble
tension. We reproduced a local void through a perturbed FLRW metric with a
potential $\Phi$ which depends on both time and space. This method allowed us
to obtain a perturbed luminosity distance, which is compared with both local
and cosmological data. We got a region of local parameters, $q_0^\text{Lo}$ and
$j_0^\text{Lo}$, which are in agreement with a local void of
$\Omega_{m,\text{void}}=-0.30\pm 0.15$ explaining the differences between the
local $H_0$ and the Planck $H_0$. However, when constraining local cosmological
parameters with previous results, we found that neither $\Lambda$CDM nor
$\Lambda(\omega)$CDM could solve the Hubble tension.
