  Hydrodynamic derivation of the entrainment of matter induced by a surface
elastic wave propagating along the flexible vacuum-matter interface is
conducted by considering the nonlinear coupling between the interface and the
rarefaction effect. The critical reflux values associated with the product of
the second-order (unit) body forcing and the Reynolds number (representing the
viscous dissipations) decrease as the Knudsen number (representing the
rarefaction measure) increases from zero to 0.1. We obtained the critical
bounds for matter-freezed or zero-volume-flow-rate states corresponding to
specific Reynolds numbers (ratio of wave inertia and viscous dissipation
effects) and wave numbers which might be linked to the evolution of the
Universe. Our results also show that for positive evolution of the matter (the
maximum speed of the matter (gas) appears at the center-line) there might be
existence of negative pressure.
