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 $\alpha_e$.
