The optimal Pad\'{e} polynomial for reconstruction of luminosity distance based on 10-fold cross-validation

TL;DR

This paper introduces a 10-fold cross-validation scheme to select the optimal Padé polynomial for reconstructing luminosity distance, demonstrating its effectiveness on Pantheon+ data and identifying the (2,1) Padé as optimal.

Contribution

The paper proposes a novel scheme for selecting the best Padé polynomial order for luminosity distance reconstruction using cross-validation, applied to cosmological data.

Findings

The scheme effectively distinguishes between Padé approximations of different orders.

The (2,1) Padé approximation is identified as optimal for Pantheon+ data.

The method improves model selection for cosmological observations.

Abstract

The cosmography known as the Pad\'{e} polynomials has been widely used in the reconstruction of luminosity distance, and the orders of Pad\'{e} polynomials influence the reconstructed result derived from Pad\'{e} approximation. In this paper, we present a more general scheme of selecting optimal Pad\'{e} polynomial for reconstruction of luminosity distance based on 10-fold cross-validation. Then the proposed scheme is applied to Pantheon+ dataset. The numerical results clearly indicate that the proposed procedure has a remarkable ability to distinguish Pad\'{e} approximations with different orders for the reconstruction of the luminosity distance. We conclude that the (2,1) Pad\'e approximation is the optimal approach that can well explain Pantheon+ data at low and high red-shifts. Future applications of this scheme could help choose the optimal model that is more suitable for cosmological observation data at hand and gain a deeper understanding of the universe.