$p-$forms non-minimally coupled to gravity in Randall-Sundrum scenarios

Abstract: In this paper we study the coupling of $p$-form fields with geometrical tensor fields, namely Ricci, Einstein, Horndeski and Riemann in Randall-Sundrum scenarios with co-dimension one. We consider delta-like and branes generated by a kink and a domain wall. We begin by a detailed study of the Kalb-Ramond (KR) field. The analysis of KR field is very rich since it is a tensorial object and more complex non-minimal couplings are possible. The generalization to $p$-forms can provide more information about the properties and structures that can possibly be universal in the geometrical localization mechanism. The zero mode is treated separately and conditions for localization of zero modes of $p-$forms are found for all the cases above and with this we arrive at the above conclusion about vector fields. Another property that can be tested is the absence of resonances found in the case of vector fields. For this we analyze the possible unstable massive modes for all the above cases via transmission coefficient. Our conclusion is that we have more probability to observe massive unstable modes in the Ricci and Riemann coupling.