Information-theoretic constraints in quantum gravity and cosmology

TL;DR

This work develops an information-theoretic framework for gravity and cosmology, using generalized entropy and quantum information tools to probe holography beyond AdS. By employing a two-dimensional JT gravity toy model, it proves quantum Bousso bounds and a restricted quantum focusing conjecture, while uncovering violations of the unrestricted QFC, motivating the restricted version as a robust semiclassical constraint. The thesis then extends holographic ideas to de Sitter and closed FLRW spacetimes via static patch holography, proposing covariant holographic entropy prescriptions (favoring bilayer constructions) and a time-dependent ER=EPR interpretation that accounts for bulk connectivity through entanglement of holographic screens. A key theme is the emergence of spacetime connectivity and causal structure from entanglement, with the connected wedge theorem serving as a stringent consistency check in non-AdS holography, including a de Sitter version proven using induced boundary causality. Collectively, these results illuminate a deep link between static patch holography, dS/CFT ideas, and cosmological holography, and propose a cohesive, information-theoretic path toward understanding quantum gravity in expanding universes.

Abstract

In this dissertation, we review results on quantum information constraints in gravity that are relevant to cosmological models and demonstrate how this approach sheds light on cosmological holography. Using Jackiw-Teitelboim gravity as a toy model, we establish the validity of the quantum Bousso bound and prove the restricted quantum focusing conjecture (rQFC), which is a central assumption in semiclassical gravity and holography. Interestingly, we find violations of the original QFC in this model. Building on these results, we introduce a covariant prescription for computing holographic entanglement entropy in the static patch holography description of de Sitter space and explore a generalization to closed FLRW spacetimes. This leads us to a formulation of subregion-subregion duality, where entanglement between complementary holographic theories gives rise to bulk connectivity. Causality considerations imply that entanglement wedges are bounded by surfaces that are not extremal in the usual sense, but instead satisfy an extremization with constraint. Finally, we discuss the connected wedge theorem, which establishes a relation between the causal structure of spacetime and information-theoretic constraints in the holographic dual. We argue that maintaining the consistency of static patch holography with this theorem leads to constraints on the causal structure of the dual theory. Our results suggest a novel relationship between static patch holography and the dS/CFT correspondence.

Figures (45)

• Figure 1: Diagrammatic picture of the (non-exhaustive) relations between different topics and statement in holography and semiclassical gravity mentioned in the introduction, with associated references. Full arrows denote a direct proof connecting the subjects or statements. Dashed arrows indicate that a statement or subject inspired or partially implies another. The shaded boxes correspond to the subjects to which this thesis contributes.
• Figure 2: A spacelike slice $\Sigma$ with endpoints $x_1=(x_1^+, x_1^-)$ and $x_2=(x_2^+, x_2^-)$ in a patch of spacetime. The right-moving modes are depicted in blue and the left-moving modes are depicted in red.
• Figure 3: Penrose diagrams of the gravity duals to the thermofield-double state in the low- and high-temperature limits. The two asymptotically AdS spacetimes are depicted in blue, with the two vertical lines being the two conformal boundaries, and the Einstein-Rosen bridge connecting them is depicted in red.
• Figure 4: Depiction of AdS$_3$, which has the topology of a cylinder. The dual CFT$_2$ is located on the boundary of the cylinder which plays the role of a holographic screen $\mathcal{S}$. A subsystem $A$ of spatial slice $\Sigma\vert_{\mathcal{S}}$ (dashed line) is depicted by the red curve. The extremal surface $\gamma_{\rm e}(A)$ is the black curve while its homology region $\mathcal{C}(A)$ is the red region.
• Figure 5: Schematic representation of the causal wedge $D(A)$ (in blue) and entanglement wedge $W(A)$ (in red) of a spacelike subsystem of the holographic screen. The boundary of $W(A)$, $\gamma_{\rm e}(A)$, always lies outside of $D(A)$ such that $D(A)\subset W(A)$.

Theorems & Definitions (47)

• Definition 2.3.1: Homology condition
• Definition 2.3.2: Extremal surface
• Definition 2.3.3: Maximin surfaces
• Theorem 2.3.1: Maximin=Extremal Wall:2012uf
• Definition 2.4.1: Entanglement wedge
• Definition 2.5.1: Island formula
• Theorem 3.2.1: Connected wedge theorem May:2019yxi
• Theorem 3.3.1: Refined connected wedge theorem
• Theorem 4.2.1: Focusing theorem
• Theorem 4.3.1: Covariant entropy bound