On supercooling and Ginzburg fluctuations in the Coleman-Weinberg mode of the SU(5) grand unification model

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We consider the supercooled SU(5) grand unified model in the Coleman-Weinberg mode, including in the lagrangian function a coupling term 1/12ξRφ2 between the field φ and the geometry, as represented by the Ricci scalar R. When the constant ξ is equal to zero, the supercooling terminates at a temperature TG>~4TH~1010 GeV, as a result of Ginzburg fluctuations, where TH = (Λ/12π2)1/2 is the temperature of the event horizon. The coupling term stabilizes the symmetric vacuum state; in the case of a conformal coupling, for which φ = 1, the universe cools down to the horizon temperature TH, at which it remains until quantum tunnelling effects the transition to the vacuum state, as described by Hawking and Moss. We estimate the critical value of φ, above which Ginzburg fluctuations do not operate, to be φc~1/2. Some cosmological consequences are discussed.

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