  There is something unknown in the cosmos. Something big. Which causes the
acceleration of the Universe expansion, that is perhaps the most surprising and
unexpected discovery of the last decades, and thus represents one of the most
pressing mysteries of the Universe. The current standard $\Lambda$CDM model
uses two unknown entities to make everything fit: dark energy and dark matter,
which together would constitute more than 95% of the energy density of the
Universe. A bit like saying that we have understood almost nothing, but without
openly admitting it. Here we start from the recent theoretical results that
come from the extension of general relativity to antimatter, through CPT
symmetry. This theory predicts a mutual gravitational repulsion between matter
and antimatter. Our basic assumption is that the Universe contains equal
amounts of matter and antimatter, with antimatter possibly located in cosmic
voids, as discussed in previous works. From this scenario we develop a simple
cosmological model, from whose equations we derive the first results. While the
existence of the elusive dark energy is completely replaced by gravitational
repulsion, the presence of dark matter is not excluded, but not strictly
required, as most of the related phenomena can also be ascribed to
repulsive-gravity effects. With a matter energy density ranging from $\sim5%$
(baryonic matter alone, and as much antimatter) to $\sim25%$ of the so-called
critical density, the present age of the Universe varies between about 13 and
$15\rm\,Gyr$. The SN Ia test is successfully passed, with residuals comparable
with those of the $\Lambda$CDM model in the observed redshift range, but with a
clear prediction for fainter SNe at higher $z$. Moreover, this model has
neither horizon nor coincidence problems, and no initial singularity is
requested. In conclusion, we have replaced all the tough problems of the
current
