New generalizations of cosmography inspired by the Padé approximant

The current accelerated expansion of the universe has been one of the most important fields in physics and astronomy since 1998. Many cosmological models have been proposed in the literature to explain this mysterious phenomenon. Since the nature and cause of the cosmic acceleration are still unknown, model-independent approaches to study the evolution of the universe are welcome. One of the powerful model-independent approaches is the so-called cosmography. It only relies on the cosmological principle, without postulating any underlying theoretical model. However, there are several shortcomings in the usual cosmography. For instance, it is plagued with the problem of divergence (or an unacceptably large error), and it fails to predict the future evolution of the universe. In the present work, we try to overcome or at least alleviate these problems, and we propose two new generalizations of cosmography inspired by the Padé approximant. One is to directly parameterize the luminosity distance based on the Padé approximant, while the other is to generalize cosmography with respect to a so-called y_β-shift y_β= z/ (1 + βz) , which is also inspired by the Padé approximant. Then we confront them with the observational data with the help of the Markov chain Monte Carlo (MCMC) code emcee, and find that they work fairly well.