  We apply the theory of open-quantum systems to describe light emission from
coherently driven molecular polaritons. Based on the microscopic Hamiltonian
that commonly describes the pure dephasing of isolated molecules, we show that
under strong-coupling conditions dephasing leads to a transfer of energy
between the constituted polariton branches $|\pm\rangle$. When the polariton
dephasing is properly accounted for, the transition from the upper to the lower
polariton branch is favored and leads to a dominant population of the lower
polariton branch under coherent pumping conditions. As a result, the inelastic
light emission originates mainly from the lower polariton state regardless of
the pumping laser frequency thus producing an asymmetric emission of light.
Furthermore, we show that, when several molecules are considered,
inter-molecular coupling breaks the symmetry of the system, making the
originally dark polaritons to effectively interact with light. This effect is
revealed in the fluorescence spectrum as new emission peaks.
