Beyond generalized Proca theories

TL;DR

This paper extends generalized Proca theories with higher-order derivatives, ensuring ghost-free conditions and analyzing perturbations, revealing differences in scalar sound speed compared to existing theories.

Contribution

It introduces new higher-order derivative interactions in Proca theories, maintaining stability and propagating degrees of freedom similar to previous models, with novel scalar sound speed behavior.

Findings

Existence of a Hamiltonian constraint removing Ostrogradski ghosts.

Same number of propagating degrees of freedom as generalized Proca theories.

Scalar sound speed differs from standard models, especially outside the Proca domain.

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.