Does incidence of appearance of quantum fluctuation particles being lowered due to space expansion?

1. in volume of space some amount of virtual particles appears during 1 second


2. amount of matter and energy in universe is constant (pls. correct me if I'm wrong)


3. space (universe) is expanding

question: will be the amount of appeared virtual particles during 1 second due to space expansion remain the same in future in same volume?

I understand that it is probably impossible to give an answer on basis of experiment. But what theory say?