Non-Relativistic Formation of Scalar Clumps as a Candidate for Dark
  Matter
  We propose a new mechanism for the formation of dark matter clumps in the
radiation era. We assume that a light scalar field is decoupled from matter and
oscillates harmonically around its vacuum expectation value. We include
self-interactions and consider the nonrelativistic regime. The scalar dynamics
are described by a fluid approach where the fluid pressure depends on both
quantum and self-interaction effects. When the squared speed of sound of the
scalar fluid becomes negative, an instability arises and the fluctuations of
the scalar energy-density field start growing. They eventually become nonlinear
and clumps form. Subsequently, the clumps aggregate and reach a universal
regime. Afterwards, they play the role of cold dark matter. We apply this
mechanism first to a model with a negative quartic term stabilised by a
positive self-interaction of order six, and then to axion monodromy, where a
subdominant cosine potential corrects a mass term. In the first case, the
squared speed of sound becomes negative when the quartic term dominates,
leading to a tachyonic instability. For axion monodromy, the instability starts
very slowly after the squared speed of sound first becomes negative and then
oscillates around zero. Initially the density perturbations perform acoustic
oscillations due to the quantum pressure. Eventually, they start growing
exponentially due to a parametric resonance.
  In both scenarios, the scalar-field clumps span a wide range of scales and
masses, running from the size of atoms to that of galactic molecular clouds,
and from $10^{-3} \, {\rm gram}$ to thousands of solar masses. Because of
finite-size effects, both from the source and the lens, these dark matter
clumps are far beyond the reach of microlensing observations.
