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

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.

Figures (9)

• Figure 1: The allowed region for $\Lambda_{\text{UV}}/ f$ as a function of ${p_{\Lambda}}$, shown as the shaded area, is derived from the unitarity bound imposed by the purity $\gamma_{\phi}$ in flat spacetime.
• Figure 2: The allowed region for $\Lambda_{\text{UV}}/ f$ as a function of ${p_{\Lambda}}$, shown as the shaded area, is derived from the unitarity bound imposed by the purity $\gamma_{\sigma}$ in flat spacetime.
• Figure 3: The allowed region for $\Lambda_{\text{UV}}/ f$ and $H/f$ as a function of ${\bar{p}_{\Lambda}}$, shown as the shaded area, is derived from the unitarity bound imposed by the purity $\gamma_{\phi}({\bar{p}_{\Lambda}})$ in de Sitter spacetime. The gray region indicates $\Lambda_{\text{UV}} \le H$, which is beyond our interests.
• Figure 4: The allowed region for $\Lambda_{\text{UV}}/ f$ and $H/f$: those for $p_\mathrm{phys} = H$ and $p_\mathrm{phys} = \Lambda_{\text{UV}}$ are illustrated. Their overlap satisfies the bounds for all $p_{\mathrm{phys}}$ within the range $H \le p_\mathrm{phys} \le \Lambda_{\text{UV}}$.
• Figure 5: The allowed region for $\Lambda_{\text{UV}}/ f$ and $H/f$ as a function of ${\bar{p}_{\Lambda}}$, shown as the shaded area, is derived from the unitarity bound imposed by the purity $\gamma_{\sigma}({\bar{p}_{\Lambda}})$ in de Sitter spacetime. The gray region indicates $\Lambda_{\text{UV}} \le H$, which is beyond our interests.