Galactic rotation curves in hybrid metric-Palatini gravity
  Generally, the dynamics of test particles around galaxies, as well as the
corresponding mass deficit, is explained by postulating the existence of a
hypothetical dark matter. In fact, the behavior of the rotation curves shows
the existence of a constant velocity region, near the baryonic matter
distribution, followed by a quick decay at large distances. In this work, we
consider the possibility that the behavior of the rotational velocities of test
particles gravitating around galaxies can be explained within the framework of
the recently proposed hybrid metric-Palatini gravitational theory. The latter
is constructed by modifying the metric Einstein-Hilbert action with an $f(R)$
term in the Palatini formalism. It was shown that the theory unifies local
constraints and the late-time cosmic acceleration, even if the scalar field is
very light. In the intermediate galactic scale, we show explicitly that in the
hybrid metric-Palatini model the tangential velocity can be explicitly obtained
as a function of the scalar field of the equivalent scalar-tensor description.
The possibility of constraining the form of the scalar field and the parameters
of the model by using the stellar velocity dispersions is also analyzed.
Furthermore, the Doppler velocity shifts are also obtained in terms of the
scalar field. All the physical and geometrical quantities and the numerical
parameters in the hybrid metric-Palatini model can be expressed in terms of
observable/measurable parameters, such as the tangential velocity, the baryonic
mass of the galaxy, the Doppler frequency shifts, and the stellar dispersion
velocity, respectively. Therefore, the obtained results open the possibility of
testing the hybrid metric-Palatini gravitational models at the galactic or
extra-galactic scale by using direct astronomical and astrophysical
observations.
