Abstract
We investigate the effects of the spacetime curvature and extra dimensions on the excitations of the Lorentz violating bumblebee field B μ . By assuming the bumblebee field living in a five-dimensional AdS 5 bulk, we found an exponential suppression of the bumblebee self-interacting constant λ and of the bumblebee vacuum expectation value (VEV) b M along the fifth extra dimension. The fluctuations of the bumblebee field upon the VEV can be decomposed into transverse and longitudinal modes with respect to b M . For a spacelike b M along the extra dimension and assuming a thin FRW 3-brane embedded in the AdS 5, the transverse mode is localized on the brane. The bulk geometry leads to a propagating and unbound longitudinal mode along the extra dimension. On the brane, the cosmological expansion leads to the decay of the longitudinal mode in time, as Δt ≈ H −1.
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