Vector theories in cosmology

Esposito-Farèse, Gilles; Pitrou, Cyril; Uzan, Jean-Philippe

Vector theories in cosmology

Journal Article

2010

Journal Title

Physical Review D - Particles and Fields

Link to Journal

https://dx.doi.org/10.1103/PhysRevD.81.063519

Department

Department of Mathematics and Applied Mathematics

Faculty

Faculty of Science

Abstract

This article provides a general study of the Hamiltonian stability and the hyperbolicity of vector field models involving both a general function of the Faraday tensor and its dual, $f(F2,Ftilde F)$, as well as a Proca potential for the vector field, $V(A2)$. In particular it is demonstrated that theories involving only $f(F2)$ do not satisfy the hyperbolicity conditions. It is then shown that in this class of models, the cosmological dynamics always dilutes the vector field. In the case of a nonminimal coupling to gravity, it is established that theories involving $R f(A2)$ or $Rf(F2)$ are generically pathologic. To finish, we exhibit a model where the vector field is not diluted during the cosmological evolution, because of a nonminimal vector field-curvature coupling which maintains second-order field equations. The relevance of such models for cosmology is discussed. Comment: 17 pages, no figure