An Information Paradox and Its Resolution in de Sitter Holography

TL;DR

This work formulates a de Sitter analogue of the information paradox within the DS/dS holographic framework and shows that entanglement islands produce a time-dependent Page curve without giving up a massless graviton. By employing double holography, the authors place a tensionless Randall-Sundrum–like brane and compute a quantum extremal surface that terminates the naive growth of entanglement entropy, yielding S_A = (1/4G_3) min(D, 2β_*) and a late-time Page saturation tied to GH entropy. The analysis extends to general dimensions and relies on a double-holographic setup in which static/distant and global descriptions distribute microscopic degrees of freedom differently, yet remain consistent with unitarity. The results offer insight into how interior regions and holographic entanglement structures emerge in quantum gravity and bolster the island paradigm in weakly gravitating regimes.

Abstract

We formulate a version of the information paradox in de Sitter spacetime and show that it is solved by the emergence of entanglement islands in the context of the DS/dS correspondence; in particular, the entanglement entropy of a subregion obeys a time-dependent Page curve. Our construction works in general spacetime dimensions and keeps the graviton massless. We interpret the resulting behavior of the entanglement entropy using double holography. It suggests that the spatial distribution of microscopic degrees of freedom depends on descriptions, as in the case of a black hole. In the static (distant) description of de Sitter (black hole) spacetime, these degrees of freedom represent microstates associated with the Gibbons-Hawking (Bekenstein-Hawking) entropy and are localized toward the horizon. On the other hand, in a global (effective two-sided) description, which is obtained by the quantum analog of analytic continuation and is intrinsically semiclassical, they are distributed uniformly and in a unique semiclassical de Sitter (black hole) vacuum state.

Figures (4)

• Figure 1: The Penrose diagram of dS spacetime in the extended static patch (left) and its spatial section at $t=0$ (right). The blue and red dots represent the north and south poles at $t=0$. The green arrows represent the direction of time evolution.
• Figure 2: The $\mathbb{Z}_2$ orbifolding removes a half of dS$_d^2$. The region $A$, of which we calculate the entanglement entropy, at $t=0$ is depicted as the green shaded region on the right panel.
• Figure 3: The spatial section at $t = 0$ for $d=2$. The two intersecting dS systems are depicted as the blue circle (dS$_2^1$) and black semicircle ($\hbox{dS}_{2}^{2}/\mathbb{Z}_{2}$). The green segment represents region $A$, of which we calculate the entanglement entropy, and the cross represents the horizon at $\beta = \frac{\pi}{2}$. The holographic bulk space ($\hbox{dS}_{3}/\mathbb{Z}_{2}$) is the hemisphere bounded by dS$_2^1$.
• Figure 4: We plot $4 G_3 S_A$ for $\beta_* = \frac{\pi}{3}$ as an example. The blue and red curves represent $D$ and $2\beta_*$, respectively; see Eq. (\ref{['eq:S_A']}). The actual $4 G_3 S_A$ is given by the solid part of the curves.