Cosmography: Supernovae Union2, Baryon Acoustic Oscillation, Observational Hubble Data and Gamma Ray Bursts

In this paper, a parametrization describing the kinematical state of the universe via cosmographic approach is considered, where the minimum input is the assumption of the cosmological principle, i.e. the Friedmann-Robertson-Walker metric. A distinguished feature is that the result does not depend on any gravity theory and dark energy models. As a result, a series of cosmographic parameters (deceleration parameter $q_0$, jerk parameter $j_0$ and snap parameter $s_0$) are constrained from the cosmic observations which include type Ia supernovae (SN) Union2, the Baryon Acoustic Oscillation (BAO), the observational Hubble data (OHD), the high redshift Gamma ray bursts (GRBs). By using Markov Chain Monte Carlo (MCMC) method, we find the best fit values of cosmographic parameters in $1\sigma$ regions: $H_0=74.299^{+4.932}_{-4.287}$, $q_0=-0.386^{+0.655}_{-0.618}$, $j_0=-4.925^{+6.658}_{-7.297}$ and $s_0=-26.404^{+20.964}_{-9.097}$ which are improved remarkably. The values of $q_0$ and $j_0$ are consistent with flat $\Lambda$CDM model in $1\sigma$ region. But the value of $s_0$ of flat $\Lambda$CDM model will go beyond the $1\sigma$ region.