Interacting field theories in de Sitter space are nonunitary

It is well known that there should be a total cancellation of the IR divergences in unitary interacting field theory, such as QED and gravity. The cancellation should be at all orders between loop and tree-level contributions to cross sections. This is the crucial fact related to the unitarity of the evolution operator (S-matrix) of the underlying interacting field theory. In this paper we show that such a cancellation does not happen in de Sitter space.