From a phenomenological perspective, the expansion of the scalar-tensor theory space opens the possibility of new and attractive explanations to different open questions in cosmology and astrophysics, e.g., the nature of dark energy, dark matter and inflation. Therefore, it is feasible to increase the space of modified theories including the cases in which there is degeneracy, thus circumventing the conditions of the instability theorem of Ostrogradsky. An analysis of these theories has been carried out within the framework of non-degenerate theories (determinant of the Hessian matrix is zero). Scalar-tensor theories represent extensions of Einstein's gravity through the inclusion of a scalar field with no-minimal coupling. In the process, we found the beyond GSU2P. Thus, we were motivated to reconstruct the theory from scratch. D 94 (2016) 084041 via their equivalence to other terms through total derivatives, not all of the latter satisfying the secondary constraint, the work was not so simple as directly applying the secondary constraint to the resultant Lagrangian pieces of the old theory. Since several terms in the Lagrangian were dismissed in Phys. It is the purpose of this talk to implement this secondary constraint in GSU2P and to make more transparent the construction of the theory. D 101 (2020) 045009 that a secondary constraint, which trivializes for the generalized Proca theory but not for the SU(2) version, was needed to close the constraint algebra.

D 94 (2016) 084041, having implemented the required primary constraint to make the Lagrangian degenerate and remove one degree of freedom from the vector field in accordance with the irreducible representations of the Poincaré group. This theory was formulated for the first time in Phys. These considerations are particularly relevant for putting constraints on cosmological and gravitational effective field theories and I will provide explicit criteria to be satisfied so as to ensure causality.Īs a modified gravity theory that introduces new gravitational degrees of freedom, the generalized SU(2) Proca theory (GSU2P for short) is the non-Abelian version of the well known generalized Proca theory where the action is invariant under global transformations of the SU(2) group.

I will clarify why a mild level of superluminality is not in contradiction with causality, analyticity or Lorentz invariance and show how consistent gravitational low energy effective theories can self-protect by ensuring that any time advance and superluminality calculated within the regime of validity of the effective theory is necessarily unresolvable for such theories. Depending on the spin of the particles integrated out, the speed of gravitational waves at low energy can be either superluminal or subluminal as compared to the causal structure observed by other species. I will investigate the propagation of gravitational waves on curved spacetimes within the low energy effective field theory of gravity, where effects from heavy fields are captured by higher dimensional curvature operators.

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