New Generalizations of Cosmography Inspired by the Pade 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 Pad\'e approximant. One is to directly parameterize the
luminosity distance based on the Pad\'e approximant, while the other is to
generalize cosmography with respect to a so-called $y_\beta$-shift
$y_\beta=z/(1+\beta z)$, which is also inspired by the Pad\'e 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.
