Imperfect fluids, Lorentz violations, and Finsler cosmology

We construct a cosmological toy model based on a Finslerian structure of space-time. In particular, we are interested in a specific Finslerian Lorentz violating theory based on a curved version of Cohen and Glashow’s very special relativity. The osculation of a Finslerian manifold to a Riemannian manifold leads to the limit of relativistic cosmology, for a specified observer. A modified flat Friedmann-Robertson-Walker cosmology is produced. The analogue of a zero energy particle unfolds some special properties of the dynamics. The kinematical equations of motion are affected by local anisotropies. Seeds of Lorentz violations may trigger density inhomogeneities to the cosmological fluid.

Figure 1

Free scale potential for the analogous zero energy one-dimensional dynamics with $b>0$, $w>-1/3$; the continuous line is the FRW potential ($b=0$). Note that the model’s potential approaches $-\infty$ faster than the classical one.

Figure 2

Free scale potential for $b<0$. The zero energy particle approaching from $a\to \infty$ accelerates until it crosses the minimum of the potential $V(a_{*})$; then it decelerates until it hits the potential at the bouncing point. The model recovers FRW behavior for large values of $a$.