On the Quantum Bousso Bound in de Sitter JT gravity
Résumé
We prove the validity of the Strominger-Thompson quantum Bousso bound in the infinite class of conformal vacua of de Sitter space in semiclassical JT gravity. The Bousso-Fisher-Leichenauer-Wall quantum Bousso bound follows from an analogous derivation, requiring only initial quantum non-expansion. In this process, we show that the quantity ${2\pi k^{\mu}k^{\nu}<:T_{\mu\nu}:>-S"-\frac{6}{c}(S')^2}$ vanishes in any vacuum state, entailing a stronger version of Wall's quantum null energy condition. We derive an entropy formula in the presence of a generic class of two reflecting boundaries, in order to apply our argument to the half reduction model of de Sitter JT gravity.