Extended vectortensor theories
(40 pages)

Using an ADM decomposition, and imposing a degenercy condition which guarantees only five degrees of freedom, the most general vectortensor Lagrangian (containing at most two derivatives) is derived.

Although the quartic order beyond generalizedProca theory has already been derived elsewhere, the approach here of writing the most general secondorder kinetic term and imposing a degeneracy condition provides an interesting alternative (perhaps more explicit) derivation. Further, this construction seems to give new theories not previously contained in the beyond generalizedProca framework.

Absence of conical singularities in beyondgeneralized Proca theories
(16 pages)

When extending secondorder Horndeski theories to beyond Horndeski (specifically GLPV scalartensor) theories, there is a conical singularity whenever the extension is nontrivial at the center of any spherically symmetric body. However, when extending secondorder generalizedProca theories to beyond generalizedProca theories, the presence of an A_{0} component generally removes the conical singularity (at least in the quarticorder Lagrangian). Further, the Vainshtein mechanism from vector Galileons around compact objects is not spoiled by the new beyond generalizedProca interactions.

On curved backgrounds, a healthy massive vector field can be described by the generalizedProca theory  which yields purely secondorder equations of motion. Recently it was found that beyond generalizedProca theories exist, in which the equations of motion are higher order, but the existence of a second class constraint prevents an associated Ostrogradski ghost. One might worry that the new interactions present in these higher order theories somehow rule out phenomenologically interesting solutions like a compact, spherically symmetric body  for example by giving a conical singularity (which happens in scalartensor theories) or by spoiling the Vainshtein mechanism. Here it is shown that neither of these worries are founded up to the quartic order Lagrangian, which seems a promising indication that the full beyond generalizedProca theory might admit a description of phenomenologically interesting compact bodies.
