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Finsler geometric perspective on the bulk flow in the universe

Astronomical observations showed that there may exist a bulk flow with peculiar velocities in the universe, which contradicts with the (Λ)CDM model. The bulk flow reveals that the observational universe is anisotropic at large scales. In fact, a more reliable observation on the anisotropy of spacetime comes from the CMB power spectra. The WMAP and Planck satellites both show that there is a hemispherical power asymmetry at large-angular scales. In this paper, we propose a "wind" scenario to the bulk flow (or the anisotropy of spacetime). Under the influence of the "wind", the spacetime metric could become a Finsler structure. By resolving the null geodesic equation, we obtain the modified luminosity distance, which has a dipolar form at the leading order. Thus, the "wind" describes well the bulk flow. In addition, we perform a least-(χ^2) fit to the data of type Ia supernovae (SNe Ia) in the Union2.1 compilation. The peculiar velocity of the bulk flow has an upper limit (v_{bulk}\lesssim 4000 \rm{km/s}), which is compatible with all the existing observational values.