Does the shape of the Higgs mexican hat depend on the temperature of the universe?

Question

I am reading this paper and i wonder if it is mainstream. Does the VeV of the Higgs field evolve with time? What about the mass given to the fermions?

Answer 1

Yes and yes to your first two questions.

Fermions are massless at sufficiently high temperature when the VEV is zero and the symmetry unbroken. They acquire mass when the universe expands and cools, the VEV becomes nonzero, and the symmetry breaks.