Comprehensive cosmographic analysis by Markov Chain Method
  We study the possibility to extract model independent information about the
dynamics of the universe by using Cosmography. We intend to explore it
systematically, to learn about its limitations and its real possibilities. Here
we are sticking to the series expansion approach on which Cosmography is based.
We apply it to different data sets: Supernovae Type Ia (SNeIa), Hubble
parameter extracted from differential galaxy ages, Gamma Ray Bursts (GRBs) and
the Baryon Acoustic Oscillations (BAO) data. We go beyond past results in the
literature extending the series expansion up to the fourth order in the scale
factor, which implies the analysis of the deceleration, q_{0}, the jerk, j_{0}
and the snap, s_{0}. We use the Markov Chain Monte Carlo Method (MCMC) to
analyze the data statistically. We also try to relate direct results from
Cosmography to dark energy (DE) dynamical models parameterized by the
Chevalier-Polarski-Linder (CPL) model, extracting clues about the matter
content and the dark energy parameters. The main results are: a) even if
relying on a mathematical approximate assumption such as the scale factor
series expansion in terms of time, cosmography can be extremely useful in
assessing dynamical properties of the Universe; b) the deceleration parameter
clearly confirms the present acceleration phase; c) the MCMC method can help
giving narrower constraints in parameter estimation, in particular for higher
order cosmographic parameters (the jerk and the snap), with respect to the
literature; d) both the estimation of the jerk and the DE parameters, reflect
the possibility of a deviation from the LCDM cosmological model.
