Abstract
We consider higher-order derivative interactions beyond second-order generalized Proca theories that propagate only the three desired polarizations of a massive vector field besides the two tensor polarizations from gravity. These new interactions follow the similar construction criteria to those arising in the extension of scalar-tensor Horndeski theories to Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories. On the isotropic cosmological background, we show the existence of a constraint with a vanishing Hamiltonian that removes the would-be Ostrogradski ghost. We study the behavior of linear perturbations on top of the isotropic cosmological background in the presence of a matter perfect fluid and find the same number of propagating degrees of freedom as in generalized Proca theories (two tensor polarizations, two transverse vector modes, and two scalar modes). Moreover, we obtain the conditions for the avoidance of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations. We observe key differences in the scalar sound speed, which is mixed with the matter sound speed outside the domain of generalized Proca theories.
Highlights
General Relativity (GR) is still the fundamental theory for describing the gravitational interactions even after a century
We study the behavior of linear perturbations on top of the isotropic cosmological background in the presence of a matter perfect fluid and find the same number of propagating degrees of freedom as in generalized Proca theories
They originate from the longitudinal component of the vector field, so it is expected that the equations of motion can be written in terms of the quantities similar to those appearing in GLPV theories [13]
Summary
General Relativity (GR) is still the fundamental theory for describing the gravitational interactions even after a century. Horndeski theories [11] constitute the most general scalar– tensor interactions with second-order equations of motion In these theories there is only one scalar degree of freedom (DOF). The key point is the requirement that the longitudinal mode belongs to the class of Galileon/Horndeski theories This constitutes the generalized Proca theories up to the quintic Lagrangian on curved space–time with second-order equations of motion, which is guaranteed by the presence of non-minimal couplings to the Lovelock invariants in the same spirit as in the scalar Horndeski theories [28,29,30,31]. Its generalization to curved space–time contains the double dual Riemann tensor, which keeps the equations of motion up to second order [31] This sixth-order Lagrangian accommodates similar vector–tensor theories constructed by Horndeski in 1976 [32].
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