Perturbative unitarity bounds on field-space curvature in de Sitter spacetime: purity vs scattering amplitude

TL;DR

This paper investigates how perturbative unitarity constrains the curvature of field space in de Sitter spacetime, revealing bounds related to the Hubble scale and highlighting the thermal effects unique to de Sitter space.

Contribution

It introduces a momentum-space entanglement approach to derive unitarity bounds on field-space curvature in de Sitter space, extending previous flat space results.

Findings

Perturbative unitarity bounds are of the order of the Hubble scale.

De Sitter spacetime's thermal nature influences unitarity bounds.

Comparison with flat space approximation shows additional bounds due to curvature.

Abstract

We study perturbative unitarity bounds on the field-space curvature in de Sitter spacetime, using the momentum-space entanglement approach recently proposed by Duaso Pueyo, Goodhew, McCulloch, and Pajer. As an illustration, we perform a perturbative computation of the purity in two-scalar models and compare the resulting unitarity bounds with those obtained via a flat space approximation. In particular, we find that perturbative unitarity imposes an upper bound on the field-space curvature of the Hubble scale order, in addition to a bound analogous to the flat space result. This reflects the thermal nature of de Sitter spacetime. We also discuss generalizations to higher-dimensional field spaces.