The nonlinear power spectrum in clustering quintessence cosmologies
  We study the nonlinear evolution of density perturbations in cosmologies
where the late-time accelerated expansion is driven by a quintessence field
with vanishing speed of sound. For these models matter and quintessence
perturbations are comoving and it is possible to write a single continuity
equation for the total density fluctuations given by a weighted sum of the two
components. Including the Euler equation for the common velocity field we solve
the evolution equations for the nonlinear, total density power spectrum in the
Time-Renormalization Group approach. In fact any cosmological observable is
directly related by gravity only to the total density perturbations, with the
two components being individually unobservable. We show that the clustering of
quintessence perturbations induces small corrections with respect to the
nonlinear evolution of power spectrum in smooth quintessence models described
by the same equation of state. Such small corrections, however, contrast with
the large effect of a vanishing speed of sound on the linear growth function at
low redshift. For this reason, models with the same normalization of the linear
density power spectrum can present significantly different nonlinear
corrections depending on the value of the sound speed. Although such
differences vanish in the w \rightarrow -1, {\Lambda}CDM limit, we argue that
the relation between linear and nonlinear growth of structures should be
properly taken into account in constraining models with inhomogeneous dark
energy.
