Cosmological model with local symmetry of very special relativity and
  constraints on it from supernovae
  Based on Cohen \& Glashow's very special relativity [A. G. Cohen and S. L.
Glashow, Phys. Rev. Lett. {\bf 97} (2006) 021601], we propose an anisotropic
modification to the Friedmann-Robertson-Walker (FRW) line element. An
arbitrarily oriented 1-form is introduced and the FRW spacetime becomes of the
Randers-Finsler type. The 1-form picks out a privileged axis in the universe.
Thus, the cosmological redshift as well as the Hubble diagram of the type Ia
supernovae (SNe Ia) becomes anisotropic. By directly analyzing the Union2
compilation, we obtain the privileged axis pointing to
\((l,b)=({304^\circ}\pm{43^\circ},{-27^\circ}\pm{13^\circ})\)
(\(68\%~\rm{C.L.}\)). This privileged axis is close to those obtained by
comparing the best-fit Hubble diagrams in pairs of hemispheres. It should be
noticed that the result is consistent with isotropy at the \(1\sigma\) level
since the anisotropic magnitude is \(D=0.03\pm 0.03\).
