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 Pad$ e $ approximations with the latest Pantheon+ sample to test the cosmological principle. Based on the Pad$ e $ approximations, we first applied cosmographic constraints to different-order polynomials including third-order (Pad$ e $), fourth-order (Pad$ e $), and fifth-order (Pad$ e $) ones. The statistical analyses show that the Pad$ e $ polynomial has the best performance. Its best fits are $H_ $ = 72.53pm 0.28 km s$^ $ Mpc$^ $, $q_ $, and $j_ $. By further fixing $j_ $ = 1.00, it can be found that the Pad$ e $ polynomial can describe the Pantheon+ sample better than the regular Pad$ e $ polynomial and the usual cosmological models (including the Lambda CDM, $w$CDM, CPL, and $R_h$ = ct models). Based on the Pad$ e $ ($j_ $ = 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 circ $) and (311.1$^ circ circ $) for $q_ $ and $H_ $, respectively. These two directions are consistent with each other at a $1 confidence level, but the corresponding results of statistical isotropy analyses including isotropy and isotropy with real positions are quite different. The statistical significance of $ is stronger than that of $q_ $; that is, 4.75sigma and 4.39sigma for isotropy and isotropy with real positions, respectively. Reanalysis with fixed $q_ = -0.55$ (corresponds to $ 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.