Reconstruction of the Dark Energy equation of state from latest data:
  the impact of theoretical priors
  We reconstruct the Equation of State of Dark Energy (EoS) from current data
using a non-parametric approach where, rather than assuming a specific time
evolution of this function, we bin it in time. We treat the transition between
the bins with two different methods, i.e. a smoothed step function and a
Gaussian Process reconstruction, investigating whether or not the two
approaches lead to compatible results. Additionally, we include in the
reconstruction procedure a correlation between the values of the EoS at
different times in the form of a theoretical prior that takes into account a
set of viability and stability requirements that one can impose on models
alternative to $\Lambda$CDM. In such case, we necessarily specialize to broad,
but specific classes of alternative models, i.e. Quintessence and Horndeski
gravity. We use data coming from CMB, Supernovae and BAO surveys. We find an
overall agreement between the different reconstruction methods used; with both
approaches, we find a time dependence of the mean of the reconstruction, with
different trends depending on the class of model studied. The constant EoS
predicted by the $\Lambda$CDM model falls anyway within the $1\sigma$ bounds of
our analysis.
