Could the big bang singularity have been set into motion by a drop in the higgs field? Could the big bang have been set into motion by a drop in the energy level of the Higgs field?
 A: For the Big Bang to be set in motion by the breaking of the electroweak symmetry this requires that there was some stable state of the universe that existed at energies of around the electroweak symmetry breaking energy. While I suppose this is possible no-one I know considers it likely. It seems far more likely that any such stable state would have an energy of around the Planck energy. We have no theory of quantum gravity to describe this state so it is impossible to make a definitive statement either way.
However it has long suggested that the Higgs is responsible for inflation. So while the Higgs field didn't start the expansion it produced the exponential expansion described by the theory of inflation.
If you use the term Big Bang to describe the moment that inflation ended then you could say the Higgs field was responsible for the Big Bang. I have seen the term used this way though personally I take it to mean the singularity at time zero.
The idea that the Higgs is responsible for inflation is usually referred to as Higgs inflation. A search will find plenty of papers on the subject though I get the impression the idea has faded in popularity recently.
