Is the Universe logotropic?
  We consider the possibility that the universe is made of a single dark fluid
described by a logotropic equation of state $P=A\ln(\rho/\rho_*)$, where $\rho$
is the rest-mass density, $\rho_*$ is a reference density, and $A$ is the
logotropic temperature. The energy density $\epsilon$ is the sum of two terms:
a rest-mass energy term $\rho c^2$ that mimics dark matter and an internal
energy term $u(\rho)=-P(\rho)-A$ that mimics dark energy. This decomposition
leads to a natural, and physical, unification of dark matter and dark energy,
and elucidates their mysterious nature. The logotropic model depends on a
single parameter $B=A/\rho_{\Lambda}c^2$ where $\rho_{\Lambda}$ is the
cosmological density. For $B=0$, we recover the $\Lambda$CDM model. Using
cosmological constraints, we find that $0\le B\le 0.09425$. We consider the
possibility that dark matter halos are described by the same logotropic
equation of state. When $B>0$, pressure gradients prevent gravitational
collapse and provide halo density cores instead of cuspy density profiles, in
agreement with the observations. The universal rotation curve of logotropic
dark matter halos is consistent with the observational Burkert profile up to
the halo radius. Interestingly, if we assume that all the dark matter halos
have the same logotropic temperature $B$, we find that their surface density
$\Sigma=\rho_0 r_h$ is constant. This result is in agreement with the
observations where it is found that $\Sigma_0=141\, M_{\odot}/{\rm pc}^2$ for
dark matter halos differing by several orders of magnitude in size. Using this
observational result, we obtain $B=3.53\times 10^{-3}$. Assuming that
$\rho_*=\rho_P$, where $\rho_P$ is the Planck density, we predict $B=3.53\times
10^{-3}$, in perfect agreement with the value obtained from the observations.
