If space is expanding, from what I remember from some space documentaries, at the beginning of the universe, during the Big Bang, there was super high pressure and temperature. But that was then; now the pressure is pretty low because the universe is expanding and that matter that was compressed is now dispersed. It's kinda like inflating a balloon - at first, it's hard because the pressure inside is high, but then it gets easier and easier.
Quantum fields are even more abstract. But from what I've heard, these quantum fields also stretch with the universe. It's not like they are created anew, but rather as the universe expands, these fields stretch along with it. As for the pressure, I think that pressure at the moment of the universe's creation had an impact on these fields, but not so much now. They already exist and don't change much, unless some major cosmic event happens.
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