Extended disformal approach in the scenario of rainbow gravity

We investigate all feasible mathematical representations of disformal transformations on a space-time metric according to the action of a linear operator upon the manifold’s tangent and cotangent bundles. The geometric, algebraic, and group structures of this operator and their interfaces are analyzed in detail. Then, we scrutinize a possible physical application, providing a new covariant formalism for a phenomenological approach to quantum gravity known as rainbow gravity.

Figure 1

On top, the vector is kept and the light cone is changed. In this case, $X$ is space-like in $g$ and time-like in $\widehat{g}$. On the bottom, the light cone is kept and the vector is deformed. The original vector (red) is space-like and its deformed counterpart (yellow) is time-like.