Beyond $$f(\phi ){\mathcal {G}}$$: Gauss–Bonnet inflation with $$\mu (\phi ,X)$$

Abstract Gauss–Bonnet inflation typically affects the dynamics over an extended portion of the trajectory, making it difficult to isolate a controlled imprint at CMB scales. We consider a trajectory-selective coupling $$\mu (\phi ,X)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>X</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> that gates the Gauss–Bonnet sector in phase space, enabling the higher-curvature contribution to be localized within a finite e-fold window while remaining negligible elsewhere. We identify stable inflationary solutions consistent with this localization and enforce standard ghost and gradient stability conditions for both scalar and tensor perturbations. For these viable backgrounds we compute pivot-scale observables and examine their dependence on the overall Gauss–Bonnet strength and on the kinetic gating. The framework offers a controlled route for realizing localized higher-curvature effects with predictable consequences for CMB-scale measurements.