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 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 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, w CDM, CPL, and R h = ct models). Based on the Padé (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° −37.4 +51.4 , −18.7° −20.3 +14.7 ) and (311.1° −8.4 +17.4 , −17.53° −7.7 +7.8 ) for q 0 and H 0 , respectively. These two directions are consistent with each other at a 1 σ 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 σ and 4.39 σ for isotropy and isotropy with real positions, respectively. Reanalysis with fixed q 0 = −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.