  Recent experiments have suggested that ground state chemical kinetics can be
suppressed or enhanced by coupling the vibrational degrees of freedom of a
molecular system with a radiation mode inside an optical cavity. Experiments
show that the chemical rate is strongly modified when the photon frequency is
close to characteristic vibrational frequencies. The origin of this remarkable
effect remains unknown. In this work, we develop an analytical rate theory for
cavity-modified ground state chemical kinetics based on the
Pollak-Grabert-H\"anggi rate theory. Unlike previous work, our theory covers
the complete range of solvent friction values, from the energy-diffusion
limited to the spatial-diffusion limited regimes. We show that the chemical
reaction rate can either be enhanced or suppressed depending on the bath
friction; when bath friction is weak chemical kinetics is enhanced as opposed
to the case of strong bath friction, where chemical kinetics is suppressed.
Further, we show that the photon frequency at which maximum modification of
chemical rate is achieved is close to the reactant well, and hence resonant
rate modification occurs. In the strong friction limit the {\it resonant}
photon frequency is instead close to the barrier frequency, as obtained using
the Grote-Hynes rate theory. Finally, we observe that the rate changes (as a
function of photon frequency) are much sharper and more sizable in the weak
friction limit than in the strong friction limit, and become increasingly sharp
with decreasing well frequency.
