Note: I very well understand spontaneous symmetry breaking of global symmetries and the Higgs mechanism.
I want to know to what extent the Standard Model vacuum is made of a Bose-Einstein condensate of Higgs bosons and what evidence (or intuitions) we have to claim that. For example, for superconductors (typical example of Higgs mechanism in condensed matter), Feshbach resonance has been used to detect the Bose-Einstein condensation of Cooper pairs. Also, in the case of the Bose-Einstein condensation of Rubidium atoms first observed in the mid 1990s, there is a very well-known graph showing the velocity distribution of the atoms, with a peak at zero velocity. These observations make it clear that there were a large number of bosons (Cooper pairs and Rubidium atoms, respectively) occupying the ground state (this is what defines Bose-Einstein condensation). What is the theoretical argument or observation for the existence of a condensate of Higgs bosons in the Standard Model?
Also, in particle physics, one usually identifies a particle as an excitation from the vacuum state, how can the (true) vacuum be full of particles?
Note: Please, please, please, don't tell me that the W and Z bosons (and other particles) acquire mass by interacting with a Higgs condensate. I know the Higgs mechanism.