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 $y\equiv z/(1+z)$ and the log-redshift $ζ\equiv\ln(1+z)$. The cubic and quartic reconstructions of $q(z)$ from the DESI BAO+CMB+SNe Ia datasets indicate a clear deviation from the $Λ$CDM model at low redshift ($z<0.3$), supporting a weaker present-day cosmic acceleration than the predictions of the $Λ$CDM model. The reconstructed $q(z)$ exhibits an overall oscillatory pattern around the $Λ$CDM 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 $Λ$CDM 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 $Λ$CDM model. Nevertheless, the Bayesian evidence still favors $Λ$CDM, while the frequentist analysis indicates a $>2σ$ preference for the Lagrange-interpolation reconstructions, hinting at the existence of dynamical dark energy.