Fig. presents the τ c -dependence of k/k 0 under the resonance condition (ω c = ω 0 ), with η c = 0.05 a.u., corresponding to a Rabi splitting of Ω R ≈ 25.09 cm -1 (based on Eq. 8) or equivalently, the time scale of Rabi oscillation Ω -1 R ≈ 211.6 fs. The numerically exact HEOM results (blue open circles) show a turnover behavior on k/k 0 when increasing τ c from the lossy limit to the lossless limit. One can observe that the FGR curve using k VSC (Eq. 10, red) agrees well with the left side of the HEOM turnover curve, corresponding to the lossy regime where τ c < 100 fs. This is because when the cavity is lossy (with a small τ c ), the cavity mode thermalizes fast with the photon-loss bath, and τ c serves as a broadening parameter in the effective spectral density . The fundamental mechanism of the rate constant enhancement is the vibrational excitation |ν L ⟩ → |ν ′ L ⟩ under the influence of the effective bath (see schematic in Fig. ).