Brane stability under $$f(Q,{\mathcal {T}})$$ gravity

Abstract The focus of this paper is to investigate the behavior of a codimension-one thick brane in the modified symmetric teleparallel gravity structure $$f(Q, {\mathcal {T}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , where Q is the nonmetricity scalar and $${\mathcal {T}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> is the trace of the energy–momentum tensor. Additionally, we examine whether braneworld scenarios are stable under small tensor perturbations and identify the associated massive and resonant modes. Our results indicate that the parameters controlling the modifications to the gravitational model-specifically those affecting nonmetricity and the energy–momentum tensor-significantly influence both the location and existence of these modes.