  Here we test different models of dark energy beyond the standard cosmological
constant scenario. We start considering the CPL parameterization of the
equation of state (EOS), then we consider a dark energy scalar field
(Quintessense). Finally we consider models with dark energy at early times
(EDE). Our analysis is based on the Union2 type Ia supernovae data set, a Gamma
Ray Bursts (GRBs) Hubble diagram, a set of 28 independent measurements of the
Hubble parameter, some baryon acoustic oscillations (BAO) measurements. We
performed a statistical analysis and explore the probability distributions of
the cosmological parameters for each of the competing models. To build up their
own regions of confidence, we maximize some appropriate likelihood functions
using the Markov chain Monte Carlo (MCMC) method. Our analysis indicates that
the EDE and the scalar field quintessence are slightly favored by the present
data. Moreover, the GRBs Hubble diagram alone is able to set the transition
region from the decelerated to the accelerated expansion of the Universe in all
the tested models. Perspectives for improvements in the field with the THESEUS
mission are also described.
