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 geometry 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 parameter, 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 Pade 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.