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Historically the Higgs Mechanism (1964) was not introduced to explain the origin of mass but rather to preserve local non-abelian gauge symmetry while still having massive weak intermediate vector bosons, the W+, W- and Z particles,eventually discovered at CERN in 1983.
Do we have any reason to believe that it must be homogenous all the way to the "edge" of the universe? And as the universe expands, does the Higgs field grow apace, or does its value decline as it gets more "dilute"?
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Just how pervasive is the Higgs field?