  We investigate the influence of electron-phonon interactions on the dynamical
properties of a quantum-dot-cavity QED system. We show that non-Markovian
effects in the phonon reservoir lead to strong changes in the dynamics, arising
from photon-assisted dephasing processes, not present in Markovian treatments.
A pronounced consequence is the emergence of a phonon induced spectral
asymmetry when detuning the cavity from the quantum-dot resonance. The
asymmetry can only be explained when considering the polaritonic quasi-particle
nature of the quantum-dot-cavity system. Furthermore, a temperature induced
reduction of the light-matter coupling strength is found to be relevant in
interpreting experimental data, especially in the strong coupling regime.
