Electroweak spontaneous symmetry breaking is much harder for me to understand than the gluon-quark plasma phase transition. In the latter the physical laws remain the same and gluons and quarks just bind together below a temperature threshold because the free energy describing its thermodynamic properties presents a new single global minimum.
However, at the EWSSB the fundamental physical laws describing particle interactions (our Standard Model of particle physics) change at that phase transition. I used to think that it was just an artifact to explain the EW interactions but since the Higgs boson has been discovered and a systematic exploration of the Higgs sector is taking place at CERN, EWSSB needs to be taken seriously.
Now I wonder if there is more to the EWSSB than meets the eye. More precisely, could dark matter and dark energy be explained by this phase transition?
1.- I think that it is reasonable to consider that the electroweak spontaneous symmetry breaking was a true thermodynamic phase transition.
2.- I also think that it is also reasonable to assume that it was a "first order phase transition".
3.- I think it is also posible/probable that the isospinor scalar field (Higgs field), could have presented two different global minima, one with a zero VEV and another with a nonzero VEV when the phase transition began. Usually, first order phase transitions ocurr because a new global minimum of the free energy of the thermodynamical system appears in addition to the already existing one. These two global minima allow two different phases with different physical properties to coexist, at least for a while. As far as I know, as long as the thermodynamical system undergoing the first order phase transitions, presents two different free energy global minima, the two phases coexist everywhere, at least in the thermodynamical limit.
Nucleation and domain expansion start only later (if they do), when one of the minima becomes local and the remaining one stays global. The phase belonging to the global minimum nucleates and expands at the expenses of the one belonging to the local minima. The picture can become more complicated if the transition process from being a global minimum to becoming a local one is very fast (water supercooling would be an example).
4.- If the Higgs field still had the two global minima at present times (or a global one and a supercooled local one separated by a large free energy barrier), I think that we would have two different sets of elementary particles with different physical properties. The true gauge charges and mass values in these two sets of particles would be:
a) Color, weak isospin, weak hypercharge and zero masses. (Higgs field VEV=0). b) Color, weak isospin and EM charge and non-zero massess. (Higgs field VEV > 0).
5.- If we had the two sets of elementary particles, their interactions could be very, very weak (it is just an assumption). I take for granted that they would, at least, interact gravitationally.
6.- If all this were possible, could this explain dark matter and/or dark energy?
For example, the long-range weak forces (in the massless sector) between particles with the same Y_w and I^3_w could lead to large-scale repulsive effects (see Quantum Field Theory 2nd Edition by Lewis E. Ryder, page 306 and references therein) that could, perhaps, explain the accelerated expansion of the universe.
I apologyze in advance for posting this question in such an odd way. However, it is the only way that I have been able to express what I had in mind.
I also realize that it is paradoxical (I suppose that many will find it laughable) thinking about two sets of elementary particles abiding different physical laws, so, please do not be too harsh with me. I can follow the maths of EWSSB but when I think about the physical process (fundamental physical laws that, suddenly change/evolve? gradually change/evolve?) I feel that either there is something that I am definitely not getting right or the dynamical process of symmetry breaking is very poorly understood.
I have written the sixth point, posing a single question and rephrased everything else because, to be honest, this is the reason why I started thinking about the EW-SSB. I have been wondering for a while if a massless Higgs Standard Model that coexisted with our Standard Model could produce a set of "almost non interacting particles" that could explain the dark components of the Lambda-CDM cosmological model.
Common sense tells me that the answer is no. I am not naive enough to think that all this is likely to be right. But it should be possible (maybe even easy) to check that the whole idea is wrong because I assume that the physics of a zero mass Higgs Standard Model can be either worked out or, even better, perhaps someone has already done it. Since I have not been able to find that information and I am unable to work it out by myself, I decided to post this question.
If such a model (zero mass Higgs Standard Model) has already been developed, please, do let me know. A link would be MUCH appreciated.