At large scales and for sufficiently early times, the Dark Matter is described as the presureless perfect fluid --- dust --- non-interacting with the other fields. These features are comprised by the simple model with two scalars, one of which is the Lagrange multiplier, while the other plays the role of the velocity potential. There is a version of this scenario leading to the pure dust solutions at the background level but giving rise to the non-zero sound speed at the linear level. We associate the modified dust with the Dark Matter, and study the linear evolution of cosmological perturbations in this picture. The most prominent effect is the suppression of the power spectrum corresponding to sufficiently small wavelengths. This can be relevant in view of the missing satellites problem. For even smaller wavelengths, however, there is the enhancement in the linear power spectrum, compared to the predictions of common Warm Dark Matter Scenarios. This is the peculiarity of the evolution during the Radiation Dominated stage. We also briefly discuss clustering of the modified dust. We show that in the Newtonian limit the relevant system of equations takes the form of the adhesive gravitational models.
