The bumblebee field excitations in a cosmological braneworld

Abstract

We investigated the effects of the spacetime curvature and extra dimensions on the excitations of a self-interacting vector field known as the bumblebee field. The self-interacting quadratic potential breaks the gauge invariance and the vacuum expectation value (VEV) of the bumblebee field b M violates the local particle Lorentz symmetry. By assuming the bumblebee field living in a AdS 5 bulk, we found an exponential suppression of the self-interacting constant λ and the bumblebee VEV along the extra dimension. The fluctuations of the bumblebee upon the VEV can be decomposed into transverse and longitudinal modes with respect to b M . We employed the eikonal approximation to study the propagation of both modes. Despite the curvature, the transverse mode is still a massless Nambu-Goldstone (NG) mode and the longitudinal mode keeps its Lorentz violating mass λb 2 . For a spacelike b M along the extra dimension and assuming a FRW 3-brane embedded in the AdS 5 yields to an additional dissipative term to the longitudinal mode. The cosmological expansion leads to decay of the longitudinal mode in a time ∆t ≈ H −1 , where H = ȧ/a is the Hubble parameter and a(t) is the scale factor. For a timelike b M , the longitudinal mode does not propagate and its amplitude decays in time with a −3 .