Spatial and temporal variations of the fine-structure constant in the Finslerian universe

Recent observations show that the electromagnetic fine-structure constant, $\alpha_e$, may vary with space and time. In the framework of Finsler spacetime, we propose here an anisotropic cosmological model, in which both the spatial and temporal variations of $\alpha_e$ are allowed. Our model naturally leads to the dipole structure of $\alpha_e$, and predicts that the dipole amplitude increases with time. We fit our model to the most up-to-date measurements of $\alpha_e$ from the quasar absorption lines. It is found that the dipole direction points towards $(l,b)=(330.2^\circ\pm7.3^\circ,-13.0^\circ\pm5.6^\circ)$ in the galactic coordinates, and the anisotropic parameter is $b_0=(0.47\pm 0.09) \times10^{-5}$, which corresponds to a dipole amplitude $(7.2\pm 1.4)\times 10^{-8}$ at redshift $z=0.015$. This is well consistent with the upper limit of the variation of $\alpha_e$ measured in the Milky Way. We also fit our model to the Union2.1 type Ia supernovae, and find that the preferred direction of Union2.1 is well consistent with the dipole direction of $\alpha_e$.