Effective reheating in Gauss–Bonnet inflation with $$\mu (\phi ,X)$$ coupling

Abstract We study effective reheating in a scalar–Gauss–Bonnet inflationary model with a phase-space-dependent coupling $$\mu (\phi ,X),$$ μ ( ϕ , X ) , in which a compact field-space feature is combined with a bounded kinetic gate. The modified inflationary background determines the pivot-scale quantities and the effective energy density at the end of inflation. These quantities are then used to derive the reheating duration $$N_{\textrm{re}}$$ N re and temperature $$T_{\textrm{re}}$$ T re through the thermal-history matching relation. We first perform two fixed-pivot reference scans by varying the overall Gauss–Bonnet strength $$\lambda _{\textrm{GB}}$$ λ GB and the kinetic-gate amplitude $$g_{_X}$$ g X separately. For the reference parameter choices, increasing either parameter increases $$N_{\textrm{re}}$$ N re and decreases $$T_{\textrm{re}}$$ T re for the selected reheating equations of state. Additional benchmark calculations clarify how these variations depend on the dynamical regime of the model. In the $$\lambda _{\textrm{GB}}$$ λ GB scan, the increase in $$N_{\textrm{re}}$$ N re and the decrease in $$T_{\textrm{re}}$$ T re persist, although both variations become strongly suppressed when the coupling is more localized or when the end of inflation is controlled more strongly by the E-model potential. In the $$g_{_X}$$ g X scan, stronger field-space localization and kinetic saturation can instead lead to a slight decrease in $$N_{\textrm{re}}$$ N re and an increase in $$T_{\textrm{re}}$$ T re as $$g_{_X}$$ g X