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Interacting Field Theories in de Sitter Space are Non-Unitary

Emil T. Akhmedov, P. V. Buividovich

TL;DR

The paper argues that quantum field theory on a fixed de Sitter background exhibits non-unitarity due to non-canceling infrared divergences between tree and loop contributions. By analyzing a non-conformal two-scalar Yukawa model in $D$ dimensions and contrasting planar with global coordinates, it shows that energy is not conserved in de Sitter space, allowing mass-shell radiation and leading to IR divergences that fail to cancel. In contrast, QFT on compact spatial sections preserves energy conservation and unitarity, but the de Sitter case generically implies that the cosmological constant must decay via particle production, effectively treating de Sitter space as an open system. These results challenge the use of a de Sitter-invariant $S$-matrix and have implications for the cosmological constant problem and the stability of de Sitter backgrounds.

Abstract

It is well known that there should be a total cancellation of the IR divergences in unitary interacting field theories, 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 note we show that such a cancellation does {\it not} happen in de Sitter space.

Interacting Field Theories in de Sitter Space are Non-Unitary

TL;DR

The paper argues that quantum field theory on a fixed de Sitter background exhibits non-unitarity due to non-canceling infrared divergences between tree and loop contributions. By analyzing a non-conformal two-scalar Yukawa model in dimensions and contrasting planar with global coordinates, it shows that energy is not conserved in de Sitter space, allowing mass-shell radiation and leading to IR divergences that fail to cancel. In contrast, QFT on compact spatial sections preserves energy conservation and unitarity, but the de Sitter case generically implies that the cosmological constant must decay via particle production, effectively treating de Sitter space as an open system. These results challenge the use of a de Sitter-invariant -matrix and have implications for the cosmological constant problem and the stability of de Sitter backgrounds.

Abstract

It is well known that there should be a total cancellation of the IR divergences in unitary interacting field theories, 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 note we show that such a cancellation does {\it not} happen in de Sitter space.

Paper Structure

This paper contains 5 sections, 31 equations, 1 figure.

Table of Contents

  1. Introduction
  2. General discussion
  3. On QFT with compact spacial sections
  4. Radiation and IR divergences in de Sitter space
  5. Conclusions

Figures (1)

  • Figure 1: Real part of the integrand in (\ref{['ampmasshel']}) for different values of $M$, $m$ and $j_1$, $j_2$, $j_3$. Imaginary part is equal to zero for the first three plots. The presence of non--zero imaginary contribution to the leading amplitude is already a sign favoring that the theory in question is non--unitary.