In the previously proposed Planck aether model of a unified theory, the vacuum ground state consists of a dense assembly of positive and negative Planck masses obeying an exactly nonrelativistic law of motion. The Planck aether is superfluid, and it can without expenditure of energy form a tangle of quantized vortex filamants permitting the transmission of two types of waves: One associated with a symmetric displacement of the vortex lattice leading to gravitational waves, and one associated with an antisymmetric displacement leading to electromagnetic waves. Dirac spinors are explained in this model as excitons made up from positive and negative energy resonances of the vortex lattice. Because the number of positive and negative Planck masses is assumed to be equal, the cosmological constant is equal to zero. With the Dirac spinors formed as bound states from the Planck aether, the sum of the positive kinetic energy and negative gravitational energy must remain exactly equal to zero, resulting in ß = l as the exact value for the cosmological mass parameter. To make up for the unobserved missing mass, estimated to be about 10 times larger than the baryonic mass, it is conjectured that this mass consists of rotons, which in the superfluid Planck aether would come from the cut-off of the energy spectrum near the Planck energy. Because of their unusual dispersion relation, rotons possess a large momentum, even if their velocity vanishes. They are, for this reason, a promising candidate for the nonbaryonic dark matter, combining properties of hot and cold dark matter. The critical value Ω = 1 requires that the number density of the rotons is equal to n r ≃ 2 x 10 -25 cm -3 . This value corresponds to an average distance of separation between the rotons of the order n r -1/3 ≃ 6000 km. The small number of rotons per unit volume combined with their weak gravitational coupling constant would make it difficult to detect them directly, but the gravitational field these roton masses generate in the vicinity of galaxies could explain the observed flat rotation curves of disc galaxies. Finally, because the gravitational waves have a cut-off at the vortex lattice scale at 10 15 -10 16 GeV, there can be no singularity in the course of a gravitational collapse, as it happens for solutions of Einstein's gravitational field equations. A generalization of Einstein's gravitational field Lagrangian, taking into account the existence of a smallest wave length, rather predicts a conversion of all mass into electromagnetic (or gravitational) radiation in approaching the singularity. The predicted conversion of mass into radiation in the course of gravitational collapse may provide an explanation for the large energy release of quasars.