Localization of bulk matter fields, the hierarchy problem and corrections to Coulomb's law on a pure de Sitter thick braneworld

In this paper we investigate the localization and mass spectra of various matter fields with spin 0, 1 and 1/2 on a geometric thick brane generated by pure four-dimensional (4D) and five-dimensional positive cosmological constants without bulk scalar fields. This model possesses a 4D cosmological constant that can be made as small as one desires without fine-tuning it with the bulk cosmological constant. The Randall-Sundrum model was obtained as an analytic continuation of the flat brane limit of this braneworld configuration when the Hubble parameter disappears. We also show that within the framework of this inflating braneworld model, it is possible to formulate a mechanism for obtaining TeV mass scales from Planck ones by adding a positive thin brane, where the Standard Model fields are trapped, located at a distance y(2) from the origin, where the Planck thick brane resides. The brane separation must be of the same order as the inverse thickness parameter of the model in order for the mechanism to generate the desired hierarchy. This result is obtained by imposing the recovery of both the correct 4D gravitational couplings and the actually observed accelerated expansion of the Universe in our de Sitter braneworld. Regarding the localization of matter in the purely geometric thick braneworld, for spin-0 massless and massive scalar fields as well as for spin-1 vector fields, the potentials of the Kaluza-Klein (KK) modes in the corresponding Schrodinger equations are modified Poschl-Teller potentials, which lead to the localization of the scalar and vector zero modes on the brane as well as to mass gaps in the mass spectra. We also compute the corrections to Coulomb's law coming from massive KK vector modes. For spin-1/2 fermions, we introduce the bulk mass term MF(z)Psi(Psi) over bar in the action, and four different cases are investigated. Localization of the massless left-chiral fermion zero mode is feasible for just two cases of F(z). In the first one, we obtain Schrodinger equations with modified Poschl-Teller potentials with the corresponding mass gaps for both left-and right-chiral fermions; the number of massive KK bound states is finite (determined by the ratio M/b) and is the same for left-and right-chiral modes. In the second case, we get a family of solutions with an infinite number of bound states where the mass spectra for left-and right-chiral KK fermion modes are discrete. A special case resembles the one-dimensional quantum harmonic oscillator problem. For both of these cases, the mass spectrum of right-chiral fermions is shifted with respect to the mass spectrum of the left-chiral ones.