The optimal Pad\'{e} polynomial for reconstruction of luminosity distance based on 10-fold cross-validation
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.
Keywords
Cite
@article{arxiv.2507.08695,
title = {The optimal Pad\'{e} polynomial for reconstruction of luminosity distance based on 10-fold cross-validation},
author = {Bo Yu and Wenhu Liu and XiaoFeng Yang and Tong-Jie zhang and Yanke Tang},
journal= {arXiv preprint arXiv:2507.08695},
year = {2025}
}
Comments
13 pages, 8 figures,1 table and accepted to APJ