Precision cosmology with Pad\'e rational approximations: theoretical
  predictions versus observational limits
  We propose a novel approach for parameterizing the luminosity distance, based
on the use of rational "Pad\'e" approximations. This new technique extends
standard Taylor treatments, overcoming possible convergence issues at high
redshifts plaguing standard cosmography. Indeed, we show that Pad\'e expansions
enable us to confidently use data over a larger interval with respect to the
usual Taylor series. To show this property in detail, we propose several Pad\'e
expansions and we compare these approximations with cosmic data, thus obtaining
cosmographic bounds from the observable universe for all cases. In particular,
we fit Pad\'e luminosity distances with observational data from different
uncorrelated surveys. We employ union 2.1 supernova data, baryonic acoustic
oscillation, Hubble space telescope measurements and differential age data. In
so doing, we also demonstrate that the use of Pad\'e approximants can improve
the analyses carried out by introducing cosmographic auxiliary variables, i.e.
a standard technique usually employed in cosmography in order to overcome the
divergence problem. Moreover, for any drawback related to standard cosmography,
we emphasize possible resolutions in the framework of Pad\'e approximants. In
particular, we investigate how to reduce systematics, how to overcome the
degeneracy between cosmological coefficients, how to treat divergences and so
forth. As a result, we show that cosmic bounds are actually refined through the
use of Pad\'e treatments and the thus derived best values of the cosmographic
parameters show slight departures from the standard cosmological paradigm.
Although all our results are perfectly consistent with the $\Lambda$CDM model,
evolving dark energy components different from a pure cosmological constant are
not definitively ruled out.
