Vector disformal transformation of generalized Proca theory
Abstract
Motivated by the GW170817/GRB170817A constraint on the deviation of the speed of gravitational waves from that of photons, we study disformal transformations of the metric in the context of the generalized Proca theory. The constraint restricts the form of the gravity Lagrangian, the way the electromagnetism couples to the gravity sector on cosmological backgrounds, or in general a combination of both. Since different ways of coupling matter to gravity are typically related to each other by disformal transformations, it is important to understand how the structure of the generalized Proca Lagrangian changes under disformal transformations. For disformal transformations with constant coefficients we provide the complete transformation rule of the Lagrangian. We find that additional terms, which were considered as beyond generalized Proca in the literature, are generated by the transformations. Once these additional terms are included, on the other hand, the structure of the gravity Lagrangian is preserved under the transformations. We then derive the transformation rules for the sound speeds of the scalar, vector and tensor perturbations on a homogeneous and isotropic background. We explicitly show that they transform following the natural expectation of metric transformations, that is, according to the transformation of the background lightcone structure. We end by arguing that inhomogeneities due to structures in the universe, e.g., dark matter halos, generically changes the speed of gravitational waves from its cosmological value. Therefore, even if the propagation speed of gravitational waves in a homogeneous and isotropic background is finetuned to that of light (at linear level), the model is subject to further constraints (at nonlinear level) due to the presence of inhomogeneities. We give a rough estimate of the effect of inhomogeneities and find that the finetuning should not depend on the background or that the finetuned theory has to be further finetuned to pass the tight constraint.
 Publication:

Physical Review D
 Pub Date:
 September 2018
 DOI:
 10.1103/PhysRevD.98.064037
 arXiv:
 arXiv:1807.06048
 Bibcode:
 2018PhRvD..98f4037D
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
 Phys. Rev. D 98, 064037 (2018)