In this work, we investigate gravitational resonances in both single and double mimetic thick branes, which can provide a new way to detect the extra dimension. For the single brane model, we apply the relative probability proposed in [Phys. Rev. D 80 (2009) 065019]. For the double brane model, we investigate the resonances quasi-localized on the double brane, on the sub-branes and between the sub-branes, respectively. To investigate the resonances quasi-localized on the double brane, we introduce two different definitions of the relative probability and find that the corresponding mass spectra of gravitational resonances are almost the same. For the gravitational resonances quasi-localized on sub-branes and between the sub-branes, the influence of the distance between the two sub-branes and the thickness of the sub-branes are analyzed and new features are found in both cases.

In this paper, we investigate thick branes generated by a scalar field in mimetic gravity theory, which is inspired by considering the conformal symmetry under the conformal transformation of an auxiliary metric. By introducing two auxiliary super-potentials, we transform the second-order field equations of the system into a set of first-order equations. With this first-order formalism, several types of analytical thick brane solutions are obtained. Then, tensor and scalar perturbations are analyzed. We find that both kinds of perturbations are stable. The effective potentials for the tensor and scalar perturbations are dual to each other. The tensor zero mode can be localized on the brane while the scalar zero mode cannot. Thus, the four-dimensional Newtonian potential can be recovered on the brane.

In this work, we study the gravitational quasinormal modes of the thick brane in Rastall gravity. Using the asymptotic iteration and direct integration methods, we solve the quasinormal frequencies of the Rastall thick brane. We also obtained the waveforms of these quasinormal modes through numerical evolution. The results indicate that although the Rastall thick brane lacks a bound zero mode, when the Rastall parameter λ ≳ 0, a long-lived quasinormal mode appears. This long-lived quasinormal mode may restore the four-dimensional effective Newtonian potential on the brane on a large scale. This may provide a new perspective for the localization of gravity on thick branes, that a thick brane does not necessarily require the gravity to be localized, perhaps quasi-localized is sufficient.

In this work, thick branes in Rastall gravity are investigated. Three types of maximally symmetric thick brane models are constructed and the linear tensor perturbation is analyzed. In the flat brane model, the tensor modes of the perturbation are either unstable or nonlocalizable for a nonvanishing Rastall parameter. In the de Sitter brane model, only the ground state of the tensor mode is localized. In the anti-de Sitter brane model, the number of the bound tensor states is infinity. For both the de Sitter and anti-de Sitter brane models, the condition of stability for the Rastall parameter is obtained. The linear scalar perturbations are also considered for the three brane models.

By adopting the idea of Born–Infeld electromagnetism, the Born–Infeld determinantal gravity in Weitzenböck spacetime provides a way to smooth the Big Bang singularity at the classical level. We consider a thick braneworld scenario in the higher-dimensional extension of this gravity, and investigate the torsion effects on the brane structure and gravitational perturbation. For three particular parameter choices, analytic domain wall solutions are obtained. They have a similar brane configuration that the brane thickness becomes thinner as the spacetime torsion gets stronger. For each model, the massless graviton is localized on the brane with the width of localization decreasing with the enhancement of the spacetime torsion, while the massive gravitons propagate in the bulk and contribute a correction term proportional to $${1}/{(k r)^{3}}$$1 / ( k r ) 3 to the Newtonian potential. A sparsity constraint on the fundamental 5-dimensional gravitational scale is estimated from the gravitational experiment. Moreover, the parameter ranges in which the Kaluza–Klein gravitons are tachyonic free are analyzed.

Recently, it was found that the vector field can be naturally localized on the thick brane in chameleon gravity. In this work, we extend this study to encompass de Sitter brane scenario. We focus on the localization of q-form fields. The scalar and vector fields can be localized on the de Sitter brane, while the KR field cannot be localized. The condition for localization of the scalar and vector fields is obtained. Furthermore, we investigate the localization characteristics in two examples with given conformal factor b(φ). In the first case, the effective potentials and KK modes of the matter fields are obtained asymmetric even though the de Sitter brane has Z₂ symmetry. In the second case, volcano-like effective potentials are generated in the de Sitter brane model.