Entanglement and factorization in axion-de Sitter universes

TL;DR

This work analyzes entanglement and correlation structure for two asymptotically de Sitter universes connected by a Euclidean axion wormhole under dS/CFT. It constructs a factorized boundary Hilbert space and interprets extremal codimension-two areas as complex holographic entanglement entropy, with late-time correlators computed via geodesic methods showing finiteness due to the Euclidean saddle. The results suggest the putative boundary duals may be non-unitary and possess large Hilbert spaces, and the study includes a dimensional reduction to axion-dS JT gravity. The framework provides insights into how Euclidean wormholes encode connectivity and entanglement in dS spacetimes and offers a path toward explicit boundary duals and further holographic dictionary tests.

Abstract

We study extremal codimension-two areas and late-time bulk correlators between a pair of asymptotically de Sitter space universes connected through an Euclidean axion wormhole, in arbitrary dimensions. Assuming the validity of the de Sitter (dS)/conformal field theory (CFT) correspondence, we describe factorized Hilbert spaces for the putative boundary theories at $\mathcal{I}^+$ in each of the universes based on the asymptotically dS isometries. This allow us to we interpret the extremal areas as complex-valued holographic entanglement entropy between the microscopic duals. Later, we evaluate two-point correlation functions for heavy particles detected near $\mathcal{I}^+$. The Euclidean wormhole saddle point is responsible for finiteness of the correlators. The results are compatible with the boundary dual being non-unitary and having a large Hilbert space dimension. At last, we dimensionally reduce these geometries in terms of dilaton-gravity theory with conformally coupled matter.

Figures (6)

• Figure 1: Euclidean geometry (in blue) of the axion-dS wormhole. The range of values of the scale factor $a\in[a_{\rm min},~a_{\rm max}]$ are determined by the roots of (\ref{['eq:derivative r, tau']}).
• Figure 2: HH preparation of the axion-dS universes constructed by slicing the geometry twice at (a) $a=a_{\rm max}$; (b) $a=a_{\rm min}$ (shown with different relative scales), (c) both $a=a_{\rm max}$ and $a=a_{\rm min}$. The Euclidean saddle is shown with blue lines, and its Lorentzian evolution is in black, and a cyan disk bipartitioning the system. The resulting universes flow with an inverted arrow of time one from the other (black arrow), describing bouncing cosmologies.
• Figure 3: Four copy HH state preparation for collapsing and expanding universes, where the expanding branches are uncoupled.
• Figure 4: Spatially closed FLRW universes with an ultra-stiff fluid evolving between bounce to a inflating cosmologies coupled at $t=0$ though the Euclidean wormhole. Given that the arrows of time evolve in opposite directions, the system can be represented in a single Penrose diagram, where $\Sigma_{P/F}$ are the Cauchy surfaces where the Hilbert space $\mathcal{H}_{P/F}^{(Q)}$ of the boundary theories are defined, and $\hat{H}_{P/F}$ is the generator of translations along $\eta_{P/F}$.
• Figure 5: Correlator for very heavy fields following a geodesic (red dashed line) between points $x$ and $y$ (red dots) very near $\mathcal{I}^+$ on each axion-dS universe, and they are connected by a geodesic path to $x'$, $y'$ (blue dots) to the Euclidean wormhole.