An expanding polariton condensate is investigated under pulsed nonresonant excitation with a small laser pump spot. Far above the condensation threshold we observe a pronounced increase in the dispersion curvature, with a subsequent linearization of the spectrum and strong luminescence from a ghost branch orthogonally polarized with respect to the linearly polarized condensate emission. Polarization of both branches is understood in terms of spin-dependent polariton-polariton scattering. The presence of the ghost branch has been confirmed in time-resolved measurements. The effects of disorder and dissipation in the photoluminescence of polariton condensates and their excitations are discussed. DOI: 10.1103/PhysRevLett.115.186401 PACS numbers: 71.36.+c, 67.10.-j, 71.35.Lk, 78.67.De Exciton polaritons are composite bosons consisting of strongly coupled microcavity photons and quantumwell excitons. They are able to form a novel class of condensates (for recent reviews see, e.g., [1,2]). Despite their nonequilibrium and dissipative nature, they behave as condensates of weakly interacting bosons. Collective phenomena like condensation [3], off-diagonal long-range order [4,5], topological excitations [6], or superfluid features in the propagation of polariton flows [7] have been demonstrated in such systems. A spectacular consequence of the parametric scattering in polariton gases is the appearance of nonparabolic scattering bands, including normal branches (NBs) and ghost branches (GBs), where the latter are populated by the virtual off-branch excitonpolaritons [7,8]. Excitations of polariton condensates are expected to be characterized by linearized dispersions of the Bogoliubov-like spectra [9]. The fluid excitations at low momenta are expected to behave as collective sound waves rather than as single particles. Recently, the linear dispersion NB and the GB of a resonantly pumped polariton condensate [10] have been observed in a four-wave mixing experiment.The experiment providing direct access to the dispersion of excitations of spontaneously formed condensates in polariton systems is photoluminescence (PL) under nonresonant excitation. The nonresonant pumping can be realized with either a detuned laser or the current injection [11,12]. In the nonresonant pumping scheme, incoherent excitons are generated and then relax, subsequently feeding the reservoir and governing the dynamics of the system [13]. The relaxation of the created hot excitons involves multiple-scattering processes, which destroy the coherence and phase of the excitation; this ensures that these properties are not inherited by the condensate, in contrast to the resonant excitation case. At the same time, the incoherent reservoir causes additional decoherence [14], forming a repulsive potential [15] which shapes the condensate spatially and spectrally. Moreover, it significantly affects the excitation spectrum of the condensate [16]. Bogoliubov dispersions have been reported in this excitation scheme; however, no fingerprints of the GB have been...