Abstract
We study symmetry restoration in a curved-background metric. Massless scalar QED is considered in the de Sitter space-time. The radius of the cosmological-event horizon corresponding to the critical temperature turns out to be of the order of the Compton wave-length of the vector boson. Quite similarly, the Gross-Neveau model in the two-dimensional Schwarzschild background shows symmetry restoration when the radius of the black-hole horizon becomes comparable with the Compton wave-length of the spinor.
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