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, 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 $\Lambda\mathrm{CDM}$ model. We fit the Planck temperature angular power spectrum $\mathcal{C}^{TT}_\ell$ for 48 different half-skies, centering on 48 different directions, to search for directional dependences of the standard cosmological parameters. There are $3(2)\sigma$-level directional variations in $\Omega_bh^2$, $\Omega_ch^2$, $n_s$, $100\theta_\mathrm{MC}$, and $H_0$ $(\tau$ and $\ln(10^{10}A_s))$. 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 disfavouring the former. The best-fit dipole axes for $\Omega_bh^2$, $\Omega_ch^2$, $n_s$, $100\theta_\mathrm{MC}$, and $A_s e^{-2\tau}$ all generally align with the mean direction of $\boldsymbol{V} \equiv (b = -5.6^{+17.0{\circ}}_{-17.4}, l = 48.8^{+14.3{\circ}}_{-14.4})$, which is roughly perpendicular to the dipole of the variation in fine structure constant, and is about $45^{\circ}$ to the directions of the CMB kinematic dipole, CMB parity asymmetry, and polarization of QSOs. Our results suggest either significant violation of the cosmological principle, or previously unknown systematic errors in the standard CMB analysis.