I'm wondering what happens if the scale factor of cosmological expansion increases without limit? Will you always calculate the same quantum foam and virtual particle production rates no matter what the scale is of the universe's expansion? If particles are extended objects, then of course virtual particle pair production is effected by the stretching of space. But if particles are singularities, then space may always have the same quantum foam properties no matter how much space is stretched by cosmic expansion. What do you think?