  The unexpected discovery of the accelerated cosmic expansion in 1998 has
filled the Universe with the embarrassing presence of an unidentified "dark
energy", or cosmological constant, devoid of any physical meaning. While this
standard cosmology seems to work well at the global level, improved knowledge
of the kinematics and other properties of our extragalactic neighborhood
indicates the need for a better theory. We investigate whether the recently
suggested repulsive-gravity scenario can account for some of the features that
are unexplained by the standard model. Through simple dynamical considerations,
we find that the Local Void could host an amount of antimatter
($\sim5\times10^{15}\,M_\odot$) roughly equivalent to the mass of a typical
supercluster, thus restoring the matter-antimatter symmetry. The antigravity
field produced by this "dark repulsor" can explain the anomalous motion of the
Local Sheet away from the Local Void, as well as several other properties of
nearby galaxies that seem to require void evacuation and structure formation
much faster than expected from the standard model. At the global cosmological
level, gravitational repulsion from antimatter hidden in voids can provide more
than enough potential energy to drive both the cosmic expansion and its
acceleration, with no need for an initial "explosion" and dark energy.
Moreover, the discrete distribution of these dark repulsors, in contrast to the
uniformly permeating dark energy, can also explain dark flows and other
recently observed excessive inhomogeneities and anisotropies of the Universe.
