Fig. presents the numerical simulations of the rate constant from HEOM as well as the FGR results. Fig. presents 𝑘(𝑡) for the resonant case when 𝜔 c = 𝜔 0 , at various light-matter coupling strengths 𝜂 c . One can clearly see the plateau value of 𝑘(𝑡) increases as 𝜂 c increases. Fig. presents the case where 𝜔 c < 𝜔 0 where 𝜔 c = 1000 cm -1 , and there is no apparent 𝜂 c dependence of 𝑘(𝑡), indicating that there is no effect of coupling to the cavity. Fig. presents the value of 𝑘/𝑘 0 (scaled by 0.4) as changing 𝜔 c using Eq. 30, depicted by the thick solid lines. A range of light-matter coupling strength 𝜂 c is explored. The FGR expression shows the sharp resonance behavior of the VSC-modified rate profile at 𝜔 c = 𝜔 0 = 1190 cm -1 . A similar sharp resonance has been observed in VSC experiments and quantum dynamics simulations . Further, we provide the rate constant calculated from the numerically exact HEOM simulations (see Sec. VII of the Supplementary Material), depicted by the open circles with a thin guiding line. Although the analytic FGR expression overestimates the rate constant by about two times, the overall agreement between the FGR expression and the HEOM numerical results is remarkable, across the range of 𝜔 c and 𝜂 c we explored.