Predictions from the logotropic model: the universal surface density of
  dark matter halos and the present proportion of dark matter and dark energy
  The logotropic model [P.H. Chavanis, Eur. Phys. J. Plus {\bf 130}, 130
(2015)] may be an interesting alternative to the $\Lambda$CDM model. It is able
to account for the present accelerating expansion of the universe while solving
at the same time the core-cusp problem of the CDM model. In the logotropic
model, there is a single dark fluid. Its rest-mass plays the role of dark
matter and its internal energy plays the role of dark energy. We highlight two
remarkable predictions of the logotropic model. It yields cored dark matter
halos with a universal surface density equal to $\Sigma_0^{\rm th}=0.01955
c\sqrt{\Lambda}/G=133\, M_{\odot}/{\rm pc}^2$ without free parameter in very
good agreement with the observational value $\Sigma_0^{\rm
obs}=141_{-52}^{+83}\, M_{\odot}/{\rm pc}^2$. It also predicts the present
ratio of dark energy and dark matter to be the pure number $\Omega_{\rm
de,0}^{\rm th}/\Omega_{\rm dm,0}^{\rm th}=e=2.71828...$ in very good agreement
with the observations giving $\Omega_{\rm de,0}^{\rm obs}/\Omega_{\rm
dm,0}^{\rm obs}=2.669\pm 0.08$. Using the measured present proportion of
baryonic matter $\Omega_{\rm b,0}^{\rm obs}=0.0486\pm 0.0010$, we find that the
values of the present proportion of dark matter and dark energy are
$\Omega_{\rm dm,0}^{\rm th}=\frac{1}{1+e}(1-\Omega_{\rm b,0})=0.2559$ and
$\Omega_{\rm de,0}^{\rm th}=\frac{e}{1+e}(1-\Omega_{\rm b,0})=0.6955$ in very
good agreement with the observational values $\Omega_{\rm dm,0}^{\rm
obs}=0.2589\pm 0.0057$ and $\Omega_{\rm de,0}^{\rm obs}=0.6911\pm 0.0062$
within the error bars. These theoretical predictions are obtained by advocating
a mysterious strong cosmic coincidence (dubbed "dark magic") implying that our
epoch plays a particular role in the history of the universe.
