Imprint of a Steep Equation of State in the growth of structure
  We study the cosmological properties of a dynamical of dark energy (DE)
component determined by a Steep Equation of State (SEoS)
$w(z)=w_0+w_i\frac{(z/z_T)^q}{1+(z/z_T)^q}$. The SEoS has a transition at $z_T$
between two pivotal values ($w_i, w_0$) which can be taken as an early time and
present day values of $w$ and the steepness is given by $q$. We describe the
impact of this dynamical DE at background and perturbative level. The steepness
of the transition has a better cosmological fit than a conventional CPL model
with $w=w_0+w_a(1-a)$. Furthermore, we analyze the impact of steepness of the
transition in the growth of matter perturbations and structure formation. This
is manifest in the linear matter power spectrum, $P(k)$, the logarithmic growth
function, $f\sigma_8(z)$, and the differential mass function $dn/d\log M(z=0)$.
The differences in these last three quantities is at a percent-level using the
same cosmological baseline parameters in our SEoS and a $\Lambda CDM$ model.
However, we find an increase in the power spectrum, producing a bump at
$k\approx k_T$ with $k_T\equiv a_TH(a_T)$ the mode associated to the time of
the steep transition ($a_T = 1/(1+z_T)$). Different dynamics of DE lead to a
different amount of DM at present time which has an impact in Power Spectrum
and accordingly in structure formation.
