Braneworlds in Einstein-Scalar-Gauss–Bonnet gravity

Abstract We explore the features of a thick braneworld model in five dimensions governed by a Einstein–Gauss–Bonnet gravity with a non-minimal coupling to a dynamical scalar field. We consider two possible scalar-GB coupling function $$\chi (\phi )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>χ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , one parity-even and another parity-odd function of the scalar field $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> . For both choices, the scalar-Gauss–Bonnet non-minimal coupling produces a warped asymptotically $$AdS_5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mi>d</mml:mi> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>5</mml:mn> </mml:msub> </mml:mrow> </mml:math> spacetime even in the absence of a bulk cosmological constant. Outside the brane core, a negative cosmological constant is bounded by the scalar-GB coupling function. For a thick 3-brane configuration, we found solutions with localized brane energy density and pressure that dynamically produce a bulk cosmological constant. The corresponding scalar field solutions exhibit a non-topological (domain wall) behavior. In order to probe the 3-brane stability solution, we employed a perturbative analysis, by perturbing the thick brane solutions up to first-order. The Kaluza–Klein (KK) tensorial gravitational modes possess a localized massless mode and a tower of non-tachyonic diverging massive modes, what renders the solutions stable at least at the perturbative level.