  In the in-/out-state formalism we find the exact one-loop effective action of
a massive scalar field in the global coordinates of de Sitter spaces, which is
a gravity analog of the Heisenberg-Euler action in QED. The nonperturbative
effective action, modulo the angular momentum sum, has an imaginary part in all
even dimensions, but the imaginary part of the effective action is zero in all
odd dimensions. However, in the zeta-function regularization for angular
momenta, the weak-curvature expansion of the renormalized effective action
vanishes in any even dimension, while the real part is finite in any odd
dimension. This implies that de Sitter spaces may be stable against particle
production at one-loop.

High Energy Physics - Theory;General Relativity and Quantum Cosmology