  We present Finslerian perturbation for the $\Lambda$CDM model, which breaks
the isotropic symmetry of the universe. The analysis on the Killing vectors
shows that the Randers-Finsler spacetime breaks the isotropic symmetry even if
the scalar perturbations of the FRW metric vanish. In Randers-Finsler
spacetime, the modified geodesic equation deduces a modified Boltzmann
equation. We propose a perturbational version of the gravitational field
equation in Randers-Finsler spacetime, where we have omitted the curvature
tensor that does not belong to the base space of the tangent bundle. The
gravitational field equations for the gravitational wave are also presented.
The primordial power spectrum of the gravitational wave is investigated. We
show that the primordial power spectrum for super-horizon perturbations is
unchanged. For sub-horizon perturbations, however, the power spectrum is
modified.
