General Very Special Relativity is Finsler Geometry

Understand

We ask whether Cohen and Glashow's Very Special Relativity model for Lorentz violation might be modified, perhaps by quantum corrections, possibly producing a curved spacetime with a cosmological constant.

• We show that its symmetry group ISIM(2) does admit a 2-parameter family of continuous deformations, but none of these give rise to non-commutative translations analogous to those of the de Sitter deformation of the Poincar\'e group: spacetime remains flat.
• Only a 1-parameter family DISIM_b(2) of deformations of SIM(2) is physically acceptable.
• Since this could arise through quantum corrections, its implications for tests of Lorentz violations via the Cohen-Glashow proposal should be taken into account.