Nonstandard approach to gravity for the dark sector of the Universe
  We summarize the present state of research on the darkon fuid as a model for
the dark sector of the Universe. Nonrelativistic massless particles are
introduced as a realization of the Galilei group in an enlarged phase space.
The additional degrees of freedom allow for a nonstandard, minimal coupling to
gravity respecting Einstein's equivalence principle. Extended to a
self-gravitating fluid the Poisson equation for the gravitational potential
contains a dynamically generated effective gravitational mass density of either
sign. The equations of motion (EOMs) contain no free parameters and are
invariant w.r.t. Milne gauge transformations. Fixing the gauge eliminates the
unphysical degrees of freedom. The resulting Lagrangian possesses no free
particle limit. The particles it describes, darkons, exist only as fluid
particles of a self-gravitating fluid. This darkon fluid realizes the zero-mass
Galilean algebra extended by dilations with dynamical exponent z = 5/3. We
reduce the EOMs to Friedmann-like equations, derive conserved quantities and a
unique Hamiltonian dynamics by implementing dilation symmetry. By the Casimir
of the Poisson-bracket (PB)-algebra we foliate the phase space and construct a
Lagrangian in reduced phase space. We solve the Friedmann-like equations with
the transition redshift and the value of the Casimir as integration constants.
We obtain a deceleration phase for the early Universe and an acceleration phase
for the late Universe in agreement with observations. Steady state equations in
the spherically symmetric case may model a galactic halo. Numerical solutions
of a nonlinear differential equation for the gravitational potential lead to
predictions for the dark matter (DM) part of the rotation curves (RCs) of
galaxies in qualitative agreement with observational data. We also present a
general covariant generalization of the model.
