Disformal symmetry in the Universe: mimetic gravity and beyond

Abstract Symmetries play an important role in fundamental physics. In gravity and field theories, particular attention has been paid to Weyl (or conformal) symmetry. However, once the theory contains a scalar field, conformal transformations of metric can be considered subclass more general type transformation, so-called disformal transformation. Here, we investigate implications pure symmetry Universe. We derive form invariant tensors from which build most action. argue that, cosmology, amounts require that lapse function is fully replaced by (time-like) at level then show exactly equivalent formulation mimetic gravity. Lastly, go beyond find class invariance leads seemingly Ostrogradski-like (with higher derivatives) Lagrangians, are nevertheless absent Ostrogradski ghosts cosmological background, despite having additional degree freedom. also propose application our formalism new invertible transformations, where coefficient involves derivatives curvature, further expanding space scalar-tensor theories.