Directional variations of cosmological parameters from the Planck CMB data

Recent observations suggest that there are violations of the isotropy of the Universe at large scales, which is an important part of the cosmological principle. In this paper, we use the cosmic microwave background (CMB) data to search for spatial variations of the cosmological parameters in the ACDM model. We fit the Planck temperature angular power spectrum ClTT for 48 different half-skies, centering on 48 different directions, to search for directional dependences of the standard cosmological parameters. There are 3[2]??-level directional variations in abh2, ach2, ns, 100??MC, and H0 [?? and ln(1010As)]. Furthermore, the directional distributions of the parameters follow a dipole form to good approximation. The Bayes factor between the isotropic and anisotropic hypotheses is 0.0041, strongly disfavoring the former. The best-fit dipole axes for abh2, ach2, ns, 100??MC, and Ase???2?? all generally align with the mean direction of V ??? (l = 48.8??14.3 ???14.4 ??; b = ???5.6??17.0 variation in the fine-structure constant, and is about 45?? to the directions of the CMB kinematic dipole, CMB parity asymmetry, and polarization of quasars. Our results suggest either a significant violation of the cosmological principle, or previously unknown systematic errors in the standard CMB analysis.