  We provide a unified theory of luminescence spectra of coupled light-matter
systems realized with semiconductor heterostructures in microcavities,
encompassing: i) the spontaneous emission case, where the system decays from a
prepared (typically pure) initial state, and ii) luminescence in the presence
of a continuous, incoherent pump. While the former case has been amply
discussed in the literature (albeit mainly for the case of resonance), no
consideration has been given to the influence of the incoherent pump. We show
how, by provoking a self-consistent quantum state, the pump considerably alters
the emission spectra, even at vanishing intensities. The main outcome of our
analysis is to unambiguously identify strong-coupling in situations where it
appears in disguise or only seems to appear. Here, we consider bosonic matter
fields, in which case fully analytical solutions can be obtained. This
describes the case of quantum wells or large quantum dots, or the limit of low
excitation where the average populations remain much smaller than one.
