The formation of the polariton states |±⟩ is readily visible in the absorption spectra of the molecule-cavity This simplified picture, however, does not reveal the true complexity of the cavity-molecule hybrid systems. The molecular excitations are not truly degenerate in energy (thus the broadening of the absorption spectra in Fig. ), and their energies fluctuate in time due to their dependence on the nuclear motion. The nuclear motion also induces non-adiabatic transitions between the upper polariton, lower polariton, and dark states, which in turn modify nuclear dynamics. Thus, direct dynamical simulations are an appealing approach to investigating the complex dynamical interplay between photons, molecular vibrations, and electronic degrees of freedom.