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# Comprehensive cosmographic analysis by Markov Chain Method

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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.
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Data
October 2013
... where the cosmographical parameters (Capozziello et al. 2011): Hubble parameter H, deceleration parameter q, jerk parameter j, snap parameter s, and lerk parameter l are defined as ...
Preprint
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... Interestingly, some cosmographic analyses lead to deviations from the concordance model, see e.g. [51] and [52,53]. In these works, it is shown that on pure cosmographic grounds the confidence level at which we may claim that the Universe is currently accelerating is moderate, if we rely on the data on SnIa+CCH only, whereas it is very strong when BAOs are also included. ...
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... The z-redshift method is the earliest Taylor series used in cosmology. The luminosity distance can be conveniently expressed as (Cattoën & Visser 2007;Capozziello et al. 2011), where H 0 , q 0 , j 0 , s 0 , and l 0 are the current values. The first two terms above are Weinberg's version of the Hubble law which can be found from equation (14.6.8) in the book by Weinberg (1972). ...
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