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We discuss the most general Finsler spacetime geometry obeying thecosmological symmetry group $\mathrm{SO}(4)$. On this background geometry wederive the equations of motion for the most general kinetic fluid obeying thesame cosmological symmetry. For this purpose we propose a set of coordinates onthe tangent bundle of the spacetime manifold which greatly simplifies thecosmological symmetry generators.

Finsler fluid dynamics in $\mathrm{SO}(4)$ symmetric cosmology