the entire theory of the higgs field and its discovery came from understanding that the model without it lacked sufficient gravity to match the world around us.
So I understand what you're saying, I disagree that we don't know how these to relate to each other. The reason Peter Higgs theorized the higgs field is because we have some idea of it.Maybe it gets more complicated than we understand currently, but we understood it enough to guess some properties of the higgs boson and discover it experimentally.
> the entire theory of the higgs field and its discovery came from understanding that the model without it lacked sufficient gravity to match the world around us.
No, it didn't. Mass is not required for gravity; only energy is. The energy was there before the electroweak phase transition; it just wasn't in the form of rest mass. It still produced gravity.
The end of the electroweak epoch is estimated at 10^-12 seconds after the big bang. So while I understand that something existed prior to the universe as we understand it now, for the overwhelming majority of the existence of reality we have lived in a reality after the electroweak phase transition, and the universe we live in today and the features we recognize of it are a result of forces including the effect of the higgs field on mass and thus gravity.
So you're right technically, but it has nothing to do with what I said in my first comment - without the higgs field the universe as we know it today would be unrecognizable, and a universe without a higgs field would not look like ours.
No. The electroweak phase transition had no effect on gravity whatever; the stress-energy that was governing the expansion was the same before and after. Again, the source of gravity in GR is the stress-energy tensor, not rest mass.
The first term is describing the rest mass. You can redefine the mass term to make it E=mc^2 but now this mass does not correspond to the rest mass. And for sure you can have energy without having a rest mass. Actually for the early universe all you had was a form of radiation and energy.
> the model without it lacked sufficient gravity to match the world around us
True, but 99% of the rest mass of a Proton comes from the gluon field, not the Higgs mechanism. The universe wouldn’t fly apart without the Higgs field.
