Geometrical deformation of brane matter field within $f(R,Q,P)$ gravity

TL;DR

This paper explores how quadratic curvature invariants in $f(R,Q,P)$ gravity affect the structure and matter field localization of a thick brane in a higher-dimensional universe, including scalar and fermionic fields.

Contribution

It introduces a detailed analysis of a codimension-one thick brane in $f(R,Q,P)$ gravity, focusing on the impact of quadratic invariants on scalar field solutions and matter localization.

Findings

Quadratic invariants influence scalar field configurations.

Normalizable zero-modes for fermions and gravitino are achieved.

Energy density profiles are affected by the geometric invariants.

Abstract

In the context of braneworld scenarios, the real scalar field plays a crucial role by providing thickness for brane. In this work, we investigate a codimension-one thick brane within the framework of $f(R,Q,P)$ gravity, where $R$ represents the curvature scalar, while $Q=R_{\mu\nu}R^{\mu\nu}$ and $P=R_{\mu\nu\alpha\beta}R^{\mu\nu\alpha\beta}$ are quadratic geometric invariants. Our interest is to investigate the influence of these invariants on the scalar field solution and the energy density of the brane. Furthermore, we analyze the localization of spin $1/2$ fermions and the gravitino by employing a Yukawa-like coupling with the scalar field background. Such a coupling is able to produce a normalizable zero-mode for both fields.