What can cause the Higgs field to exist in a way that it can cover the entire universe?
That’s a good question. I could say: we don’t know. But that’s a lousy answer. In fact, it’s not just the Higgs field that we believe covers all of space. ALL fields stretch infinitely far, at least according to quantum field theory, even electron, photon, and quark fields. It’s just that MOST fields, all the other ones besides the Higgs field, are zero over most of space hence they might as well not really be there. An electron field is peaked around the atom where it sits and is very very small everywhere else. The odd thing about the Higgs field is thus not that it fills all of space, but that it is non-zero over all of space. We believe this was not always so, and that it has to do with a symmetry that was broken in the early universe. In the beginning, the Higgs field was probably zero everywhere, or at least its average was zero (there are always quantum fluctuations around the average, and in the very early universe those can be pretty big). The Universe later underwent a phase
