Possible Improvements Of Cosmography Based On The Padé Approximant

At the end of the 1990 s, the universe was found to go through an accelerated expansion by using type Ia supernovae(SNIa) as standard candle. With the continuous development of astronomical observation, baryon acoustic oscillations(BAO) and cosmic microwave background(CMB) radiation also demonstrate this point. There are two approach to explain this phenomenon: Dark energy cosmology and the modified gravity. Both dark energy models and modified gravity theories seem to be concent with data, the physical mechanism from which this cosmic speed up originates is still unclear, therefore, we want to find an approach which is model independent to describe the status of universe. Cosmography is used to analyze the dynamics of the universe without postulating any underlying theoretical model, the only assumption is the cosmological principle, i.e. the Friedmann-Robertson-Walker metric. The standard cosmography is common to expand physical quantities as Taylor series in the cosmological redshift z. Here we are interested in the luminosity distance versue redshift relation. The standard cosmography has some shortcomings: first, the Taylor serious non-convergent at z ≥ 1. Secondly, it could not describe the future of the universe well.Different parameterizations of the redshift variable has been proposed, but they are still not fully applicable. As is known, any function can be expanded by Padé approximation, and it can avoid the divergence problem in the higher-order terms of Taylor expansion. Inspired by the Padé approximant, we propose a new parameterization yβ= z/(1 + βz). Similarly we express the luminosity distance as function of yβ. By using a new Markov chain Monte Carlo(MCMC) method-emcee, we compare this yβ-based cosmography with cosmic data which include type Ia supernovae(SN) Union2.1 and the cosmic microwave background(CMB) to constrain model parameters.