  We investigate theoretically nonequilibrium effects on photoluminescence and
gain/absorption spectra of a driven-dissipative exciton-polariton condensate,
by employing the combined Hartree-Fock-Bogoliubov theory with the generalized
random phase approximation extended to the Keldysh formalism. Our calculated
photoluminescence spectra is in semiquantitative agreement with experiments,
where features such as a blue shift of the emission from the condensate, the
appearance of the dispersionless feature of a diffusive Goldstone mode, and the
suppression of the dispersive profile of the mode are obtained. We show that
the nonequilibrium nature of the exciton-polariton condensate strongly
suppresses the visibility of the Bogoliubov dispersion in the negative energy
branch (ghost branch) in photoluminescence spectra. We also show that the trace
of this branch can be captured as a hole burning effect in gain/absorption
spectra. Our results indicate that the nonequilibrium nature of the
exciton-polariton condensate strongly reduces quantum depletion, while a
scattering channel to the ghost branch is still present.
