International audienceWe present a numerically complete study of the combined dynamics of a quantum dot exciton coupled to a single quantized cavity mode and a continuum of acoustic phonons. We demonstrate that acoustic phonons have a pronounced impact on effects characteristic of the strong light-matter coupling regime, such as vacuum Rabi oscillations and collapse and revival scenarios. This impact is considerable already at zero temperature, where initially no phonons are present. Counterintuitively it is found that an increase of the light-matter coupling does not necessarily enhance the visibility of strong-coupling effects. In fact, for typical experimental situations, a stronger light-matter coupling will considerably reduce the visibility