The bumblebee field excitations in a cosmological braneworld

¹ Universidade Federal do Ceará (UFC), Departamento de Física - Campus do Pici, Fortaleza, CE, C.P. 6030, 60455-760, Brazil
² Universidade Federal do Cariri (UFCA) - Av. Tenente Raimundo Rocha, Cidade Universitária, Juazeiro do Norte, Ceará, CEP 63048-080, Brazil

^(a) E-mail: euclides.silva@ufca.edu.br (corresponding author)

Received: 20 September 2022
Accepted: 16 December 2022

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 AdS₅ 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 AdS₅, 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.