Primordial Black Holes and Induced Gravitational Waves from Inflation with History-Dependent Effective Dissipation

We study inflation with an exponential factor multiplying the scalar Lagrangian and depending on the accumulated expansion history through a field-dependent coupling. Variation of the complete action on a finite interval yields an adjoint response with a final-time boundary condition. We derive the background and coupled scalar perturbation equations and examine five benchmarks for an exponential plateau potential and a smooth single-window coupling. The kinetic, direct-coupling and adjoint contributions nearly cancel, producing transient positive minima of the first Hubble slow-roll parameter, ε₁, without a comparable reduction in field velocity. The scalar spectra, normalized to the cosmic microwave background (CMB) pivot amplitude, develop localized peaks with amplitudes $0.033$--$0.098$. Under Gaussian statistics and the adopted radiation-era collapse prescription, the the primordial black hole (PBH) abundance peaks span masses from 4.52×10⁻¹³ to 34.05\,M_. The lightest-mass benchmark reaches fPBH0.99, allowing nearly all dark matter within the monochromatic approximation. The accompanying scalar-induced gravitational-wave spectra span peak frequencies from 6.78×10⁻¹⁰ to 5.92×10⁻³\,Hz, with selected benchmarks lying within the projected sensitivities of future detectors.