Testing cosmic anisotropy with Pade approximation and Pantheon+ sample

Cosmography can be used to constrain the kinematics of universe in a model-independent way. In this work, we attempted to combine the Pade approximations with the latest Pantheon+ sample for testing cosmological principle. Based on the Pade approximations, we first gave the cosmographic constraints on the different order polynomials including third-order (Pade(2,1)$), fourth-order (Pad$ {e}(2,2)) and fifth-order (Pade(3,2)$). Based on the Pad$ {e}(2,1) (j₀ = 1) polynomial and hemisphere comparison (HC) 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 in 1σ confidence level, but the corresponding results of statistical isotropy analyses including Isotropy and Isotropy with real positions (RP) are quite different. The statistical significance of H₀ are stronger than that of q₀, i.e., 4.75σ and 4.39σ for the Isotropy and Isotropy with RP respectively. Reanalysis with fixed q₀ = -0.55 (corresponds to Ωₘ = 0.30) gives similar results. Overall, our model-independent results provide clear indications for a possible cosmic anisotropy, which must be taken seriously. Further test is needed to better understand this signal.