  In this paper we investigate the localization and mass spectra of matter
fields with spin 0, 1 and 1/2 on a geometric thick brane generated by pure 4D
and 5D 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 RS model is
obtained as an analytic continuation of the flat brane limit of this braneworld
configuration when the Hubble parameter disappears. Within 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, at a distance y_2 from the origin, where the Planck
thick brane resides. The brane separation must be of the same order than 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 thecorresponding Schroedinger
equations are modified Poeschl-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)\bar{\Psi}\Psi in the action and show that localization of
the massless left-chiral fermion zero mode is feasible for two mass functions
MF(z) with a finite/infinite number of massive KK bound states.
