Non-comoving baryons and cold dark matter in cosmic voids
  We examine the fully relativistic evolution of cosmic voids constituted by
baryons and cold dark matter (CDM), represented by two non-comoving dust
sources in a $\Lambda$CDM background. For this purpose, we consider numerical
solutions of Einstein's field equations in a fluid-flow representation adapted
to spherical symmetry and multiple components. We present a simple example that
explores the frame-dependence of the local expansion and the Hubble flow for
this mixture of two dusts, revealing that the relative velocity between the
sources yields a significantly different evolution in comparison with that of
the two sources in a common 4-velocity (which reduces to a
Lemaitre-Tolman-Bondi model). In particular, significant modifications arise
for the density contrast depth and void size, as well as in the amplitude of
the surrounding over-densities. We show that an adequate model of a
frame-dependent evolution that incorporates initial conditions from peculiar
velocities and large-scale density contrast observations may contribute to
understand the discrepancy between the local value of $H_0$ and that inferred
from the CMB.
