Precision cosmology with Padé rational approximations: theoretical predictions versus observational limits

Abstract

We propose a novel approach for parameterizing the luminosity distance, based on the use of rational "Padé" approximations. This new technique extends standard Taylor treatments, overcoming possible convergence issues at high redshifts plaguing standard cosmography. Indeed, we show that Padé 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 Padé expansions and we compare these approximations with cosmic data, thus obtaining cosmographic bounds from the observable universe for all cases. In particular, we fit Padé 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 Padé 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 Padé 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 Padé 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.

24 pages, 9 figures

References in corpus (14)

• Dynamics of dark energy
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• Spectra and Light Curves of Six Type Ia Supernovae at 0.511 < z < 1.12 and the Union2 Compilation
• Reconstructing Dark Energy
• Baryon Acoustic Oscillations in the Ly-α forest of BOSS quasars
• Nonparametric Dark Energy Reconstruction from Supernova Data
• The Dynamics of Quintessence, The Quintessence of Dynamics
• The Hubble series: Convergence properties and redshift variables
• Nonparametric Reconstruction of the Dark Energy Equation of State
• Reconstruction of the Dark Energy equation of state
• Crossing Statistic: Reconstructing the Expansion History of the Universe
• Bayesian Evidence for a Cosmological Constant using new High-Redshift Supernovae Data
• Holographic Gas as Dark Energy

Cited by in corpus (7)

• Extended Gravity Cosmography
• Viscous Cosmology for Early- and Late-Time Universe
• Cosmology with gamma-ray bursts: II Cosmography challenges and cosmological scenarios for the accelerated Universe
• Model-independent reconstruction of $f(T)$ teleparallel cosmology
• Connecting early and late universe by $f(R)$ gravity
• Model-Independent Constraints on Lorentz Invariance Violation via the Cosmographic Approach
• A numerical approach to model independently reconstruct $f(R)$ functions through cosmographic data