Probing a Steep EoS for Dark Energy with latest observations
  We present a parametrization for the Dark Energy Equation of State "EoS"
which has a rich structure, performing a transition at pivotal redshift $z_T$
between the present day value $w_0$ to an early time $w_i=w_a+w_0\equiv
w(z\gg0)$ with a steepness given in terms of $q$ parameter. The proposed
parametrization is $w=w_0+w_a(z/z_T)^q/(1+(z/z_T))^q$, with $w_0$, $w_i$, $q $
and $z_T$ constant parameters. It reduces to the widely used EoS
$w=w_0+w_a(1-a)$ for $z_T=q=1$. This transition is motivated by scalar field
dynamics such as for example quintessence models. We study if a late time
transition is favored by BAO measurements combined with local determination of
$H_0$ and information from the CMB. According to our results, an EoS with a
present value of $w_0 = -0.92$ and a high redshift value $w_i =-0.99$,
featuring a transition at $z_T = 0.28$ with an exponent $q = 9.97$ was favored
by data coming from local dynamics of the Universe (BAO combined with $H_0$
determination). We find that a dynamical DE model allows to simultaneously fit
$H_0$ from local determinations and Planck CMB measurements, alleviating the
tension obtained in a $\Lambda$CDM model.
  Additionally to this analysis we solved numerically the evolution of matter
over-densities in the presence of dark energy both at background level and when
its perturbations were considered. We show that the presence of a steep
transition in the DE EoS gets imprinted into the evolution of matter
overdensities and that the addition of an effective sound speed term does not
erase such feature.
