Modified Dust and the Small Scale Crisis in CDM
  At large scales and for sufficiently early times, dark matter is described as
a pressureless perfect fluid---dust---non-interacting with Standard Model
fields. These features are captured by a simple model with two scalars: a
Lagrange multiplier and another playing the role of the velocity potential.
That model arises naturally in some gravitational frameworks, e.g., the mimetic
dark matter scenario. We consider an extension of the model by means of higher
derivative terms, such that the dust solutions are preserved at the background
level, but there is a non-zero sound speed at the linear level. We associate
this {\it Modified Dust} with dark matter, and study the linear evolution of
cosmological perturbations in that picture. The most prominent effect is the
suppression of their power spectrum for sufficiently large cosmological
momenta. This can be relevant in view of the problems that cold dark matter
faces at sub-galactic scales, e.g., the missing satellites problem. At even
shorter scales, however, perturbations of Modified Dust are enhanced compared
to the predictions of more common particle dark matter scenarios. This is a
peculiarity of their evolution in radiation dominated background. We also
briefly discuss clustering of Modified Dust. We write the system of equations
in the Newtonian limit, and sketch the possible mechanism which could prevent
the appearance of caustic singularities. The same mechanism may be relevant in
light of the core-cusp problem.
