Testing cosmic anisotropy with Pade approximations and the latest Pantheon plus 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 Pade approximations with the latest Pantheon+ sample to test the cosmological principle. Based on the Pade approximations, we first applied cosmographic constraints to different-order polynomials including third-order (Pade((2, 1))), fourth-order (Pade((2, 2))), and fifth-order (Pade((3, 2))) ones. The statistical analyses show that the Pade((2, 1)) polynomial has the best performance. Its best fits are H-0 = 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 j(0) = 1.00, it can be found that the Pade((2, 1)) polynomial can describe the Pantheon+ sample better than the regular Pade((2, 1)) polynomial and the usual cosmological models (including the Lambda CDM, wCDM, CPL, and R-h = ct models). Based on the Pade((2, 1)) (j(0) = 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 degrees(+51.4)(-37.4), -18.7 degrees(+14.7)(-20.3)) and (311.1 degrees(+17.4)(-8.4), -17.53 degrees(+7.8)(-7.7)) for q(0) and H-0, respectively. These two directions are consistent with each other at a 1 sigma confidence level, but the corresponding results of statistical isotropy analyses including isotropy and isotropy with real positions are quite different. The statistical significance of H-0 is stronger than that of q(0); that is, 4.75 sigma and 4.39 sigma for isotropy and isotropy with real positions, respectively. Reanalysis with fixed q(0) = -0.55 (corresponds to Omega(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.