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04 September, 2016

posted 4 Sep 2016, 02:46 by Scott Melville   [ updated 4 Sep 2016, 02:46 ]
Extended vector-tensor theories
(40 pages)

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


Although the quartic order beyond generalized-Proca theory has already been derived elsewhere, the approach here of writing the most general second-order 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 generalized-Proca framework.

Absence of conical singularities in beyond-generalized Proca theories
(16 pages)

When extending second-order Horndeski theories to beyond Horndeski (specifically GLPV scalar-tensor) theories, there is a conical singularity whenever the extension is non-trivial at the center of any spherically symmetric body. However, when extending second-order generalized-Proca theories to beyond generalized-Proca theories, the presence of an A0 component generally removes the conical singularity (at least in the quartic-order Lagrangian). Further, the Vainshtein mechanism from vector Galileons around compact objects is not spoiled by the new beyond generalized-Proca interactions.


On curved backgrounds, a healthy massive vector field can be described by the generalized-Proca theory - which yields purely second-order equations of motion. Recently it was found that beyond generalized-Proca 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 scalar-tensor 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 generalized-Proca theory might admit a description of phenomenologically interesting compact bodies.