Precision cosmology with Pad\'e rational approximations: theoretical predictions versus observational limits

TL;DR

This paper introduces Padé rational approximations for cosmological distance measurements, extending the range and accuracy of standard methods, and compares these with observational data to refine cosmographic bounds.

Contribution

It presents a novel Padé-based parameterization method for luminosity distance, improving convergence and analysis of high-redshift cosmological data over traditional Taylor series.

Findings

Padé approximations extend the usable redshift range for cosmography.

Refined cosmographic bounds from observational data using Padé methods.

Results are consistent with ΛCDM but allow for evolving dark energy models.

Abstract

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.