Cosmological scalar field perturbations can grow
  It has been argued that the small perturbations to the homogeneous and
isotropic configurations of a canonical scalar field in an expanding universe
do not grow. We show that this is not true in general, and clarify the root of
the misunderstanding. We revisit a simple model in which the zero-mode of a
free scalar field oscillates with high frequency around the minimum of the
potential. Under this assumption the linear perturbations grow like those in
the standard cold dark matter scenario, but with a Jeans length at the scale of
the Compton wavelength of the scalar particle. Contrary to previous analyses in
the literature our results do not rely on time-averages and/or fluid
identifications, and instead we solve both analytically (in terms of a
well-defined series expansion) and numerically the linearized
Einstein-Klein-Gordon system. Also, we use gauge-invariant fields, which makes
the physical analysis more transparent and simplifies the comparison with
previous works carried out in different gauges. As a byproduct of this study we
identify a time-dependent modulation of the different physical quantities
associated to the background as well as the perturbations with potential
observational consequences in dark matter models.
