Evolution of Dark Energy Perturbations in Scalar-Tensor Cosmologies
  We solve analytically and numerically the generalized Einstein equations in
scalar-tensor cosmologies to obtain the evolution of dark energy and matter
linear perturbations. We compare our results with the corresponding results for
minimally coupled quintessence perturbations. Our results for natural (O(1))
values of parameters in the Lagrangian which lead to a background expansion
similar to LCDM are summarized as follows: 1. Scalar-Tensor dark energy density
perturbations are amplified by a factor of about 10^6 compared to minimally
coupled quintessence perturbations on scales less than about 100 h^{-1} Mpc. On
these scales dark energy perturbations constitute a fraction of about 10%
compared to matter density perturbations. 2. Scalar-Tensor dark energy density
perturbations are anti-correlated with matter linear perturbations on
sub-Hubble scales. Thus clusters of galaxies are predicted to overlap with
voids of dark energy. 3. This anti-correlation of matter with negative pressure
perturbations induces a mild amplification of matter perturbations by about 10%
on sub-Hubble scales. 4. The evolution of scalar field perturbations on
sub-Hubble scales, is scale independent and therefore it corresponds to a
vanishing effective speed of sound (c_{s\Phi}=0). It also involves large
oscillations at early times induced by the amplified effective mass of the
field. This amplification is due to the non-minimal coupling of the field to
the Ricci curvature scalar and (thus) to matter. No such oscillations are
present in minimally coupled quintessence perturbations which are suppressed on
sub-Hubble scales (c_{s\Phi}=1). Implications of our results include modified
predictions for cluster halo profiles observed properties. These profiles are
known to be in some tension with the predictions of LCDM.
