Constraints on Steep Equation of State for the Dark Energy using BAO

We present a parametrization for the Dark Energy Equation of State "EoS" which has a rich structure. Our EoS has a transition at pivotal redshift $z_T$ between the present day value $w_0$ to an early time $w_i=w_a+w_0\equiv w(z>>0)$ and the steepness of this transition is given in terms of the $q$ 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. This transition is motivated by scalar field dynamics such as for example quintessence models. Our parametrization reduces to the widely used EoS $w=w_0+w_a(1-a)$ for $z_T=q=1$. We study if a late time transition is favored by BAO measurements and Planck priors. According to our results, an EoS with a present value of $w_0 = -0.91$ and a high redshifts value $w_i =-0.62$, featuring a transition at a redshift of $z_T = 1.16$ with an exponent $q = 9.95$ is a good fit to the observational data. We found good agreement between the model and the data reported by the different surveys. A "thawing" dynamics is preferred by the use of BAO data alone (including Lymman-$\alpha$ forest measurements) and a "freezing" evolution of the EoS is preferred when we include the priors from Planck. The constraints imposed by the available BAO measurements (\cite{Beutler:2011hx, Ross:2014qpa, Anderson:2013oza, Kazin:2014qga, Font-Ribera:2013wce, Delubac:2014aqe, Gong:2015tta}) and its physical behavior are discussed.