  Recent observations show that planet formation is already underway in young
systems, when the protostar is still embedded into the molecular cloud and the
accretion disc is massive. In such environments, the role of self gravity (SG)
and gravitational instability (GI) is crucial in determining the dynamical
evolution of the disc. In this work, we study the dynamical role of drag force
in self-gravitating discs as a way to form planetesimals in early
protoplanetary stages. We obtain the dispersion relation for density-wave
perturbations on a fluid composed of two phases (gas and dust) interacting
through the common gravitation field and the mutual drag force, and we find
that the stability threshold is determined by three parameters: the local
dust-to-gas density ratio, the dust relative temperature and the relevant
Stokes number. In a region of parameters space, where young protoplanetary
discs are likely to be found, the instability can be dust driven, occurring at
small wavelengths. In this regime, the Jeans mass is much smaller than the one
predicted by the standard gravitational instability model. This mechanism can
be a viable way to form planetary cores in protostellar discs, since their
predicted mass is about 10 Earth masses.
