DESI DR2 meets cosmography: a comparative study of Padé, Chebyshev, and Taylor expansions

ABSTRACT We perform a comprehensive cosmographic analysis of the late-time Universe using the latest Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) baryon acoustic oscillation (BAO) measurements, comparing Taylor, Padé, and Chebyshev expansions as model-independent reconstructions of the background expansion. We consider Padé approximants of order (2,1) and (2,2), a Chebyshev expansion, and a third-order Taylor series. Due to its limited radius of convergence, the Taylor expansion is constrained using only the low-redshift DESI sub-set ($z< 1$), while the rational Padé forms and the Chebyshev expansion are applied over the full DESI DR2 redshift range. Cosmographic parameters are inferred through a Bayesian Markov chain Monte Carlo (MCMC) analysis, and the resulting best-fitting reconstructions of $H(z)$, $d_L(z)$, and BAO distance indicators are compared with the predictions of the Lambda cold dark matter ($\Lambda$CDM) model. All methods are consistent with $\Lambda$CDM at low redshift, but the Chebyshev expansion exhibits noticeable deviations at higher redshifts, while the Padé$_{(2,1)}$ and Padé$_{(2,2)}$ reconstructions remain closely aligned with $\Lambda$CDM across the DESI DR2 range. A model-selection analysis based on Akaike Information Criterion and Bayesian Information Criterion shows a clear statistical preference for the Taylor expansion over low-z$\Lambda$CDM, and a strong preference for Padé cosmography over $\Lambda$CDM when the full DESI DR2 data set is used. These results demonstrate the constraining power of DESI DR2 for cosmographic studies and highlight the utility of rational approximants, especially Padé forms, in extending cosmography reliably to higher redshifts beyond the domain of traditional Taylor series.