High-Redshift Cosmography
  We constrain the parameters describing the kinematical state of the universe
using a cosmographic approach, which is fundamental in that it requires a very
minimal set of assumptions (namely to specify a metric) and does not rely on
the dynamical equations for gravity. On the data side, we consider the most
recent compilations of Supernovae and Gamma Ray Bursts catalogues. This allows
to further extend the cosmographic fit up to $z = 6.6$, i.e. up to redshift for
which one could start to resolve the low z degeneracy among competing
cosmological models. In order to reliably control the cosmographic approach at
high redshifts, we adopt the expansion in the improved parameter $y = z/(1+z)$.
This series has the great advantage to hold also for $z > 1$ and hence it is
the appropriate tool for handling data including non-nearby distance
indicators. We find that Gamma Ray Bursts, probing higher redshifts than
Supernovae, have constraining power and do require (and statistically allow) a
cosmographic expansion at higher order than Supernovae alone. Exploiting the
set of data from Union and GRBs catalogues, we show (for the first time in a
purely cosmographic approach parametrized by deceleration $q_0$, jerk $j_0$,
snap $s_0$) a definitively negative deceleration parameter $q_0$ up to the
3$\sigma$ confidence level. We present also forecasts for realistic data sets
that are likely to be obtained in the next few years.
