Localization of q-form field on squared curvature gravity domain wall brane coupling with gravity and background scalar

In this paper, we investigate a q-form field, represented as XM₁M₂...Mq, where q indicates the number of indices, with special cases q = 0, 1, 2 corresponding to the scalar fields, vector fields, and Kalb-Ramond fields, respectively. Unlike the duality observed between scalar and vector fields in four-dimensional spacetime, q-form fields in higher dimensions correspond to a wider array of particles. We propose a novel localized Kaluza-Klein decomposition approach for the q-form field in a five-dimensional spacetime, considering its coupling with gravity and background scalar fields. This methodology enables the successful localization of the q-form field on a domain wall brane, leading to the derivation of zero modes, Schr\"{o}dinger-like equations, and a four-dimensional effective action. Additionally, in order to stand for the coupling of the q-form field with gravity and scalar fields of the background spacetime, we propose a new coupling function F(R,φ). Our analysis highlights the significance of the parameters C₂ and t in the localization process.