Remarks on the Cosmological Constant and the $λΦ^4$ Phase Transition

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We reanalyze the problem of the cosmological constant associated with the phase transition in a self-interacting scalar theory. It is pointed out that the generally accepted ``triviality'' of $(λΦ^4)_4$ implies a first-order phase transition. As a consequence, Spontaneous Symmetry Breaking can be consistent with zero cosmological constant if one assumes that it vanishes in the symmetric phase $<Φ>=0$.
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