The universe must expand otherwise temporary local deformations would not perceive as attractive. The same mechanism that locally pumps volume into the field, will expand that field. The local addition starts spreading over the field. The mechanism is implemented by spherical pulse responses.
Stochastic processes generate the pulses. They create mass out of nothing. Here mass stands for local deformation. This deformation quickly fades away. The processes produce a continuous stream of massive objects that dilute into the increasing volume of the universe. This means that mass is a very transient property. That property must recurrently be regenerated. That is why all elementary particle are recurrently regenerated by regenerating their constituents, which are spherical pulse responses.
The embedding of the separate Hilbert spaces in which the elementary particles reside, into a non-separable Hilbert space drives the stochastic processes. Thus the volume stream comes from content of the separable Hilbert spaces that is added to the non-separable Hilbert space.