A Half de Sitter Holography

TL;DR

This work proposes a holographic framework for half de Sitter space by introducing a timelike boundary, arguing that gravity on half $dS_{d+1}$ is dual to a non-local field theory on $dS_d$ with a finite cutoff. The authors analyze holographic entanglement entropy and pseudo-entropy under two prescriptions—Schwinger-Keldysh without EOW and with an end-of-the-world brane—finding that subadditivity can be violated due to non-locality and that static time slices yield sensible Hilbert spaces while generic slices overcount degrees of freedom. They connect these geometric results to CFT calculations on $dS_2$, extend the analysis to higher dimensions, and discuss the role of EOW branes in defining a final-state projection and Page-like behavior. The findings illuminate how de Sitter holography may constrain Hilbert-space structure and entanglement, with potential implications for cosmology and non-local quantum field theories.

Abstract

A long-standing and intriguing question is: does the holographic principle apply to cosmologies like de Sitter spacetime? In this work, we consider a half dS spacetime wherein a timelike boundary encloses the bulk spacetime, presenting a version of de Sitter holography. By analyzing the holographic entanglement entropy in this space and comparing it with that in AdS/CFT, we argue that gravity on a half dS$_{d+1}$ is dual to a highly non-local field theory residing on dS$_d$ boundary. This non-locality induces a breach in the subadditivity of holographic entanglement entropy. Remarkably, this observation can be linked to another argument that time slices in global de Sitter space overestimate the degrees of freedom by redundantly counting the same Hilbert space multiple times.

Figures (28)

• Figure 1: The Penrose diagram of dS$_{d+1}$ bulk spacetime. The conformal time $T\in [-\frac{\pi}{2},+\frac{\pi}{2}]$ is associated with the global time $t$ by $\cosh t= \frac{1}{\cos T}$. We introduce a timelike boundary at $\theta=\theta_0$ which is described by a $d-$dimensional dS spacetime. The dual bulk dS$_{d+1}$ spacetime is given by the gray shaded region.
• Figure 2: The left panel shows the geometry of time slices for a global dS$_3$. In the right panel we keep a half of dS$_3$ space with a dS$_2$ boundary (denoted by green circle) at $\theta=\theta_0$.
• Figure 3: The left panel shows a sketch of global de Sitter space, which has only space-like boundaries at $t=\pm\infty$. The right one is a sketch of our holographic setup which is obtained by cutting in half a de Sitter space. Notice that this geometry has both the time-like and space-like boundary.
• Figure 4: The geometry which describes the Schwinger-Keldysh contour of a half dS$_{d+1}$. The top and bottom region presents the Lorentzian and Euclidean evolution, respectively. This is dual to a field living on dS$_d$ boundary which is parametrized by the green surface.
• Figure 5: The geometry of a half dS$_{d+1}$. Notice that there are both timelike (green surface) and spacelike (purple surface) boundaries.