Cosmological Applications of Pade Approximant

Abstract

As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.

19 pages, 8 figures, 1 table, revtex4; v2: discussions added, accepted for publication in JCAP; v3: published version

References in corpus (23)

• Dynamics of dark energy
• Dark Energy and the Accelerating Universe
• Cosmological Constraints from the SDSS Luminous Red Galaxies
• Cosmology and Fundamental Physics with the Euclid Satellite
• Report of the Dark Energy Task Force
• WMAP constraints on low redshift evolution of dark energy
• A parametric model for dark energy
• Interacting Agegraphic Dark Energy
• A generalized equation of state for dark energy
• Pilgrim Dark Energy
• Cosmological Constraints on the Modified Entropic Force Model
• A New Class of Parametrization for Dark Energy without Divergence
• Reconstructing the Cosmic Expansion History up to Redshift z=6.29 with the Calibrated Gamma-Ray Bursts
• $w$-cosmological singularities
• Interacting Energy Components and Observational $H(z)$ Data
• Revisiting the Cosmological Constraints on the Interacting Dark Energy Models
• Modified Holographic Dark Energy
• A new perspective on the relation between dark energy perturbations and the late-time ISW effect
• Is the Dynamics of Tracking Dark Energy Detectable?
• Cosmological Models and Latest Observational Data
• Numerical Strategies of Computing the Luminosity Distance
• Dark Energy Cosmology with the Alternative Cosmic Microwave Background Data
• Relaxing the Cosmological Constraints on Unparticle Dark Component

Cited by in corpus (57)

• Extended Gravity Cosmography
• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• High-redshift cosmography: auxiliary variables versus Padé polynomials
• Model independent constraints on dark energy evolution from low-redshift observations
• Precision cosmology with Padé rational approximations: theoretical predictions versus observational limits
• Cosmographic analysis with Chebyshev polynomials
• Beyond $\Lambda$CDM with Low and High Redshift Data: Implications for Dark Energy
• An overview of what current data can (and cannot yet) say about evolving dark energy
• Cosmological Models and Gamma-Ray Bursts Calibrated by Using Pade Method
• New observational constraints on $f(T)$ cosmology from radio quasars
• Connecting early and late epochs by f(z)CDM cosmography
• Global dynamics and inflationary center manifold and slow-roll approximants
• High-redshift cosmography: Application and comparison with different methods
• Pantheon update on a model-independent analysis of cosmological supernova data
• Can high-redshift Hubble diagrams rule out the standard model of cosmology in the context of cosmographic method?
• New Generalizations of Cosmography Inspired by the Pade Approximant
• Cosmographic view on the $H_0$ and ${\sigma }_8$ tensions
• Dark energy reconstruction based on the PADE approximation; an expansion around the $\Lambda$CDM
• Barotropic fluid compatible parametrizations of dark energy
• Data Analysis of three parameter models of deceleration parameter in FRW Universe
• Constraining the cosmological model of modified $f(Q)$ gravity: Phantom dark energy and observational insights
• A divergence-free parametrization for dynamical dark energy
• Cosmological Constant, Fine Structure Constant and Beyond
• Cosmographic Footprints of Dynamical Dark Energy
• A new pressure-parametrization unified dark fluid model
• Testing cosmic anisotropy with Pade approximation and Pantheon+ sample
• Observational Constraints on Growth Index with Cosmography
• Calculating Luminosity Distance versus Redshift in FLRW Cosmology via Homotopy Perturbation Method
• An exponential equation of state of dark energy in the light of 2018 CMB Planck data
• What do the cosmological supernova data really tell us?
• LADDER: Revisiting the Cosmic Distance Ladder with Deep Learning Approaches and Exploring its Applications
• Structure formation in dark energy cosmologies described by PADE parameterization
• High-redshift cosmography with a possible cosmic distance duality relation violation
• A model independent parametrization of the late time cosmic acceleration: constraints on the parameters from recent observations
• On the number of galaxies at high redshift
• Shape of Dark Energy: Constraining Its Evolution with a General Parametrization
• Joint Constraints on the Hubble Constant, Spatial Curvature, and Sound Horizon from the Late-time Universe with Cosmography
• Observational Constraints on Varying Alpha in $\Lambda (\alpha )$CDM Cosmology
• Testing dark energy models with $H(z)$ data
• Square-Root parametrization of dark energy in $f(Q)$ cosmology
• Revisiting CPL with sign-switching density: To cross or not to cross the NECB
• A numerical approach to model independently reconstruct $f(R)$ functions through cosmographic data
• Probing the Dynamics of Gaussian Dark Energy Equation of State Using DESI BAO
• Dark Energy in the DESI Era: A Brief Review of Evidence, Beyond-$\Lambda$CDM Interpretations, and Tensions
• Testing inhomogeneous cosmography in our cosmic neighborhood using CosmicFlows-4
• Bias of reconstructing the dark energy equation of state from the Pad$\acute{e}$ cosmography
• The optimal Padé polynomial for reconstruction of luminosity distance based on 10-fold cross-validation
• Effect of Peak Absolute Magnitude of Type Ia Supernovae and Sound Horizon Values on Hubble Tension using DESI results
• Is Dark Energy Changing? Probing the Universe's Expansion with present and future astronomical probes
• Padé Approximant and Minimax Rational Approximation in Standard Cosmology
• Computing the luminosity distance via optimal homotopy perturbation method
• Analysis of Pantheon+ supernova data suggests evidence of sign-changing pressure of the cosmological fluid
• Classical and relativistic evolution of an extra-galactic jet with back-reaction
• A semi-cosmographic approach to study cosmological evolution in phase space
• The dynamics of background evolution and structure formation in phase space: a semi-cosmographic reconstruction
• Testing the cosmic distance duality relation using model-independent approach
• Conservation of the Flux of Energy in Extra-Galactic Jets