Fig. presents the scaling relation between k/k 0 (at ω c = ω 0 , resonant condition) and the light-matter coupling strength η c . The open red circles represent the results obtained from the HEOM simulations (identical to Fig. ). The red curve is a fitting line for data points when η c < 0.05 (or Ω R < 25 cm -1 ). The results ob- tained from FGR (Eq. 41) are presented with a solid gold line. The FGR rate, not surprisingly, correctly predicted k/k 0 ∝ η 2 c when η c < 0.05 (or Ω R < 25 cm -1 ). Further increasing η c leads to a breakdown of the FGR, because it is only valid when Ω R k B T , where the Rabi splitting Ω R (Eq. E3) is the energy coupling term in the FGR (see Eq. E4). For the current model system, when Ω R < 25 cm -1 (η c < 0.05), FGR provides an accurate description of the basic scaling of k/k 0 . With a further increase of Ω R , the HEOM results suggests a scaling k/k 0 ∝ η n c , where n < 2 for the range of η c ∈ [0.05, 0.1]. Experimentally, the typical range of Ω R are within 200 cm -1 , and will likely observe k/k 0 ∝ 1 + η n c for n ≤ 2. Our HEOM results also suggest that further increase in the light-matter coupling strength η c will eventually lead to a saturation in the enhancement, in agreement with the previous study. Fig. presents the VSC-modified rate profile as a function of ω c , by varying cavity lifetime τ c using the same parameters as in Fig. . The open circles (and the guiding thin lines) represent the results obtained from HEOM simulations (identical to those in Fig. ), whereas the thick solid lines are results obtained from FGR (Eq. 41). Note that the FGR results are also scaled by a factor of 0.4 to provide a convenient comparison with the HEOM results. Although not perfectly reproducing the numerically exact results, the FGR rate indeed captured the basic trend of the rate profile as one gradually increases τ c for τ c < 100 fs. Fig. presents the k/k 0 at the resonant condition ω c = ω 0 , as a function of the cavity lifetime τ c . The convolved FGR expression (Eq. 41) correctly captures the linear dependence of k/k 0 at small τ c (< 100 fs) (as also predicted by Eq. 52). When further increase τ c , the current FGR theory predicts that the rate profile gradually converges to a Gaussian line shape with a variance of σ 2 (see Eq. 43), resulting in a sigmoid dependence of k/k 0 as increasing τ c (golden curve). The numerical simulations from HEOM (blue open circles), on the other hand, show a turnover behavior and start to deviate FGR for τ c > 100 fs, indicating the breakdown of the current FGR theory. This is because under the lossless limit, the cavity loss no longer plays the role of a simple (homogeneous) broadening factor, but rather the photon number excitation (see Sec. E for details). Near the lossless limit, decreasing τ c induces a stronger cavity mode-photon loss coupling (see Eq. 13), thus a faster |0 → |1 transition (for the cavity Fock states). As a result, the resonance enhancement is magnified. Rate theories that describe this interesting behavior remain to be further developed.