Testing cosmic anisotropy with Padé approximations and the latest Pantheon+ sample

¹ School of Astronomy and Space Science, Nanjing University, Nanjing, 210093 China
e-mail: hjp1206@163.com
² School of Engineering, Dali University, Dali, 671003 China
³ Research Center for Astronomical Computing, Zhejiang Lab, Hangzhou, 311100 China
⁴ Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing, 210093 China

Received: 12 April 2024
Accepted: 20 June 2024

Abstract

Cosmography can be used to constrain the kinematics of the Universe in a model-independent way. In this work, we attempt to combine the Padé approximations with the latest Pantheon+ sample to test the cosmological principle. Based on the Padé approximations, we first applied cosmographic constraints to different-order polynomials including third-order (Padé_(2, 1)), fourth-order (Padé_(2, 2)), and fifth-order (Padé_(3, 2)) ones. The statistical analyses show that the Padé_(2, 1) polynomial has the best performance. Its best fits are H₀ = 72.53 ± 0.28 km s⁻¹ Mpc⁻¹, q₀ = −0.35_−0.07^+0.08, and j₀ = 0.43_−0.56^+0.38. By further fixing j₀ = 1.00, it can be found that the Padé_(2, 1) polynomial can describe the Pantheon+ sample better than the regular Padé_(2, 1) polynomial and the usual cosmological models (including the ΛCDM, wCDM, CPL, and R_h = ct models). Based on the Padé_(2, 1) (j₀ = 1) polynomial and the hemisphere comparison method, we tested the cosmological principle and found the preferred directions of cosmic anisotropy, such as (l, b) = (304.6°_−37.4^+51.4, −18.7°_−20.3^+14.7) and (311.1°_−8.4^+17.4, −17.53°_−7.7^+7.8) for q₀ and H₀, respectively. These two directions are consistent with each other at a 1σ confidence level, but the corresponding results of statistical isotropy analyses including isotropy and isotropy with real positions are quite different. The statistical significance of H₀ is stronger than that of q₀; that is, 4.75σ and 4.39σ for isotropy and isotropy with real positions, respectively. Reanalysis with fixed q₀ = −0.55 (corresponds to Ω_m = 0.30) gives similar results. Overall, our model-independent results provide clear indications of a possible cosmic anisotropy, which must be taken seriously. Further testing is needed to better understand this signal.