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Cosmography is used in cosmological data processing in order to constrain thekinematics of the universe in a model-independent way, providing an objectivemeans to evaluate the agreement of a model with observations. In this paper, weextend the conventional methodology of cosmography employing Taylor expansionsof observables by an alternative approach using Pad\'e approximations. Due tothe superior convergence properties of Pad\'e expansions, it is possible toimprove the fitting analysis to obtain numerical values for the parameters ofthe cosmographic series. From the results, we can derive the equation of stateparameter of the universe and its first derivative and thus acquire informationabout the thermodynamic state of the universe. We carry out statisticalanalyses using observations of the distance modulus of type 1a supernovae,provided by the union 2.1 compilation of the supernova cosmology project,employing a Markov chain Monte Carlo approach with an implemented Metropolisalgorithm. We compare the results of the original Taylor approach to the newlyintroduced Pad\'e formalism. The analyses show that experimental data constrainthe observable universe well, finding an accelerating universe and a positivejerk parameter. We demonstrate that the Pad\'e convergence radii are greaterthan standard Taylor convergence radii, and infer a lower limit on theacceleration of the universe solely by requiring the positivity of the Pad\'eexpansion. We obtain fairly good agreement with the Planck results, confirmingthe $\Lambda$CDM model at small redshifts, although we cannot exclude a darkenergy density varying in time with negligible speed of sound.

Cosmographic analysis of the equation of state of the universe through Pad\'e approximations