I will discuss peculiarities of quantum fields in de Sitter space on the
example of the self-interacting massive real scalar. Non-conformal
quantum field theories in de Sitter space show very special infrared
behavior, which is not shared by quantum fields neither in flat nor in
anti-de-Sitter space: in de Sitter space loops are not suppressed in
comparison with tree level contributions and dominate at late times.
That is true even for massive fields. I will discuss how the invariance
of the quantum field theory under the de Sitter isometry gets broken due
to the loop corrections and such symmetry could be respected only by one
state. Also I will discuss how physics in even dimensional de Sitter
spaces is different from odd dimensional ones.
Based on recent works with A. Polyakov, E. Akhmedov and U. Moschella