Constraining Dark Energy Perturbations: the Role of Early Dark Energy
  Dark Energy not only has background effects through its equation of state
$w_{DE}$, but also it can cluster through its sound speed $c^2_{sDE}$, subject
to certain conditions. As is well-known, for dynamical dark energy models, dark
energy perturbations get sourced into matter perturbations through metric
perturbations which is always accompanied by the term $(1+w_{DE})$. Hence, for
dynamical dark energy models with $w_{DE}$ close $-1$, their perturbations get
almost decoupled from metric leaving nearly null imprints on matter power
spectra. Furthermore, Quintessence models with its sound speed equal to speed
of light, washes out almost any inhomogeneities occurred within sub-Hubble
scales, hence making detectability of dark energy perturbations far more
difficult than already is. In this article we look for these imprints by going
beyond Quintessence considering an Early Dark Energy parametrization that not
only have a non-negligible energy density at early times, but also it can
achieve $w_{DE}$ far from $-1$, making dark energy perturbations detectable in
sub-horizon scales. With the help of current datasets, we are able to constrain
sound speed of dark energy to a low value ($c^2_{sDE} \sim 0.14$), along with a
much higher range allowed for early dark energy density, with strong
constraints on it ($\Omega_e \sim 0.02$). We discuss effects of different
datasets on this parametrization along with possible explanation for deviation
on certain parameter(s) comparing between $c^2_{sDE}=1$ case and the case where
it is kept open.
