Reconstructing the evolution of deceleration parameter with the Lagrange interpolation method

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 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 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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BibTeX RIS

BibTeX

@misc{zhang2026reconstructing,
  title = {{Reconstructing the evolution of deceleration parameter with the Lagrange interpolation method}},
  author = {Kaituo Zhang and Bing Xu and Hongwei Yu and Puxun Wu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34239},
  eprint = {2609.34239},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34239},
}

RIS

TY  - UNPB
TI  - Reconstructing the evolution of deceleration parameter with the Lagrange interpolation method
AU  - Kaituo Zhang
AU  - Bing Xu
AU  - Hongwei Yu
AU  - Puxun Wu
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34239
UR  - https://arxiv.org/abs/2609.34239
AB  - 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 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 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 H_0 from the Supernovae and H_0 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 H_0 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.
ER  -

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