  We study the resonance fluorescence spectra of a driven quantum dot placed
inside a high $Q$ semiconductor cavity and interacting with an acoustic phonon
bath. The dynamics is calculated using a time-convolutionless master equation
obtained in the polaron frame. We demonstrate pronounced spectral broadening of
the Mollow sidebands through cavity-emission which, for small cavity-coupling
rates, increases quadratically with the Rabi frequency. However, for larger
cavity coupling rates, this broadening dependence is found to be more complex.
This field-dependent Mollow triplet broadening is primarily a consequence of
the triplet peaks sampling different parts of the asymmetric phonon bath, and
agrees directly with recent experiments with semiconductor micropillars. The
influence from the detuned cavity photon bath and multi-photon effects is shown
to play a qualitatively important role on the fluorescence spectra.
