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.

Figure 1

The real part of the integrand in (21) for different values of $M$, $m$ and $j_1$, $j_2$, $j_3$. The imaginary part is equal to zero for the first three plots. The presence of the nonzero imaginary contribution to the leading amplitude is already a sign favoring that the theory in question is nonunitary.