Cosmology with gamma-ray bursts: II Cosmography challenges and
  cosmological scenarios for the accelerated Universe
  Context. Explaining the accelerated expansion of the Universe is one of the
fundamental challenges in physics today. Cosmography provides information about
the evolution of the universe derived from measured distances, assuming only
that the space time ge- ometry is described by the
Friedman-Lemaitre-Robertson-Walker metric, and adopting an approach that
effectively uses only Taylor expansions of basic observables. Aims. We perform
a high-redshift analysis to constrain the cosmographic expansion up to the
fifth order. It is based on the Union2 type Ia supernovae data set, the
gamma-ray burst Hubble diagram, a data set of 28 independent measurements of
the Hubble param- eter, baryon acoustic oscillations measurements from galaxy
clustering and the Lyman-{\alpha} forest in the SDSS-III Baryon Oscillation
Spectroscopic Survey (BOSS), and some Gaussian priors on h and {\Omega}M .
Methods. We performed a statistical analysis and explored the probability
distributions of the cosmographic parameters. By building up their regions of
confidence, we maximized our likelihood function using the Markov chain Monte
Carlo method. Results. Our high-redshift analysis confirms that the expansion
of the Universe currently accelerates; the estimation of the jerk parameter
indicates a possible deviation from the standard {\Lambda}CDM cosmological
model. Moreover, we investigate implications of our results for the
reconstruction of the dark energy equation of state (EOS) by comparing the
standard technique of cosmography with an alternative approach based on
generalized Pad\'e approximations of the same observables. Because these
expansions converge better, is possible to improve the constraints on the
cosmographic parameters and also on the dark matter EOS. Conclusions. The
estimation of the jerk and the DE parameters indicates at 1{\sigma} a possible
deviation from the {\Lambda}CDM cosmological model.
