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 bosom Quite similarly, the Gross-Neveau model in the twodimensional
Schwarzschild background shows symmetry restoration
when the radius of the black-hole horizon becomes comparable with
the Compton wave-length of the spinor.
