In this work we study a scenario with a warped 5D smooth braneworld with 4D Minkowski geometry builded from bulk scalar matter non-minimally coupled to gravity with an additional Gauss-Bonnet term. We present exact solutions for the full braneworld c
onfiguration in contrast to previous results where only approximate solutions were constructed due to the highly non-linear character of the relevant differential equations. These solutions allow us to study the necessary conditions for the finiteness of the 4D Planck mass and additionally, enables us to perform a more rigorous analysis of 4D gravity localization compared to approximate approaches. It is remarkable that all the constructed braneworld configurations lead to standard 4D gravity localization since they contain a localized massless tensor mode (the graviton). We also analyze the localization properties of scalar, vector and tensor fluctuation modes for the constructed field configurations. We show that for the considered backgrounds, only the massless tensor mode, i.e. the 4D graviton, is localized on the brane, while the vector and scalar modes are not confined to the brane.
Among the multiple 5D thick braneworld models that have been proposed in the last years, in order to address several open problems in modern physics, there is a specific one involving a tachyonic bulk scalar field. Delving into this framework, a thic
k braneworld with a cosmological background induced on the brane is here investigated. The respective field equations --- derived from the model with a warped 5D geometry --- are highly non-linear equations, admitting a non-trivial solution for the warp factor and the tachyon scalar field as well, in a de Sitter 4D cosmological background. Moreover, the non-linear tachyonic scalar field, that generates the brane in complicity with warped gravity, has the form of a kink-like configuration. Notwithstanding, the non-linear field equations restricting character does not allow one to easily find thick brane solutions with a decaying warp factor which leads to the localization of 4D gravity and other matter fields. We derive such a thick brane configuration altogether in this tachyon-gravity setup. When analyzing the spectrum of gravity fluctuations in the transverse traceless sector, the 4D gravity is shown to be localized due to the presence of a {it single} zero mode bound state, separated by a continuum of massive Kaluza-Klein (KK) modes by a mass gap. It contrasts with previous results, where there is a KK massive bound excitation providing no clear physical interpretation. The mass gap is determined by the scale of the metric parameter $H$. Finally, the corrections to Newtons law in this model are computed and shown to decay exponentially. It is in full compliance to corrections reported in previous results (up to a constant factor) within similar braneworlds with induced 4D de Sitter metric, despite the fact that the warp factor and the massive modes have a different form.
