Prospects of high redshift constraints on dark energy models with the
  Ep- Eiso correlation in long Gamma Ray Bursts
  So far large and different data sets revealed the accelerated expansion rate
of the Universe, which is usually explained in terms of dark energy. The nature
of dark energy is not yet known, and several models have been introduced: a non
zero cosmological constant, a potential energy of some scalar field, effects
related to the non homogeneous distribution of matter, or effects due to
alternative theories of gravity. Recently, a tension with the flat {\Lambda}CDM
model has been discovered using a high-redshift Hubble diagram of supernovae,
quasars, and gamma-ray bursts. Here we use the Union2 type Ia supernovae (SNIa)
and Gamma Ray Bursts (GRB) Hubble diagram, and a set of direct measurements of
the Hubble parameter to explore different dark energy models. We use the
Chevallier-Polarski- Linder (CPL) parametrization of the dark energy equation
of state (EOS), a minimally coupled quintessence scalar field, and, finally, we
consider models with dark energy at early times (EDE). We perform a statistical
analysis based on the Markov chain Monte Carlo (MCMC) method, and explore the
probability distributions of the cosmological parameters for each of the
competing models. We apply the Akaike Information Criterion (AIC) to compare
these models: our analysis indicates that an evolving dark energy, described by
a scalar field with exponential potential seems to be favoured by observational
data.
