Constraints on barotropic dark energy models by a new phenomenological $q(z)$ parameterization

In this paper, we propose a new phenomenological two parameter parametrization of $q(z)$ to constrain barotropic dark energy models by considering a spatially flat FRW universe, neglecting the radiation component, and reconstructing the effective equation of state (EoS). This two free-parameter EoS reconstruction shows a non-monotonic behavior, pointing to a more general fitting for the scalar field models, like thawing and freezing models. We constrain the $q(z)$ free parameters using the observational data of the Hubble parameter obtained from cosmic chronometers, the joint-light-analysis type Ia Supernovae sample and a joint analysis from these data. We obtain a value of $q(z)$ today, $q_0=-0.48\substack{+0.10 \\ -0.11}$, and a transition redshift, $z_t=0.71\substack{+0.12 \\ -0.12}$ (when the Universe change from an decelerated phase to an accelerated one). The effective EoS reconstruction and the $\omega'$-$\omega$ plane analysis pointed out a quintom dark energy, which is consistent with a non parametric EoS reconstruction, reported by other authors, and using the latest cosmological observations.