  In the framework of finite temperature conformal scalar field theory on de
Sitter space-time the linearized Einstein equations for the renormalized stress
tensor are exactly solved. In this theory quantum field fluctuations are
concentrated near two spheres of the de Sitter radius, propagating as light
wave fronts. Related cosmological aspects are shortly discussed. The analysis,
performed for flat expanding universe, shows exponential damping of the
back-reaction effects far from these spherical objects. The obtained solutions
for the semiclassical Einstein equations in de Sitter background can be
straightforwardly extended also to the anti-de Sitter geometry.
