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

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, $ q_{0} = -0.35_{-0.07}^{+0.08} $, and $ j_{0} = 0.43_{-0.56}^{+0.38} $. By further fixing j0 = 1.00, it can be found that the Padé(2, 1) polynomial can describe the Pantheon+ sample better than the regular Padé(2, 1) polynomial and the usual cosmological models (including the ΛCDM, wCDM, CPL, and Rh = ct models). Based on the Padé(2, 1) (j0 = 1) polynomial and the hemisphere comparison method, we tested the cosmological principle and found the preferred directions of cosmic anisotropy, such as (l, b) = (304.6$ ^{\circ+51.4}_{-37.4} $, −18.7$ ^{\circ+14.7}_{-20.3} $) and (311.1$ ^{\circ+17.4}_{-8.4} $, −17.53$ ^{\circ+7.8}_{-7.7} $) 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 Ωm = 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.