Shocks and Information Exchange in de Sitter Space

TL;DR

This work examines information exchange and complementarity in de Sitter space by importing ideas from AdS black hole physics into a bulk de Sitter setting. It uses a thermofield double–like Bunch-Davies vacuum and isotropic shockwaves to create a traversable wormhole between antipodal static patches, enabling information to be transferred after a scrambling time $t \sim H^{-1}\log S_{ m dS}$, conditioned on an entangled energy reservoir sourced from Hawking radiation. The authors derive bounds on how much information can be transmitted and interpret the process as a Hayden-Preskill–type decoding in a cosmological context, while addressing potential cloning concerns. They discuss generalizations to higher dimensions (including Schwarzschild–de Sitter interiors) and acknowledge that a full single-observer information-recovery protocol remains an open question, offering a concrete bulk mechanism and guiding framework for cosmological information dynamics.

Abstract

We discuss some implications of recent progress in understanding the black hole information paradox for complementarity in de Sitter space. Extending recent work by two of the authors, we describe a bulk procedure that allows information expelled through the cosmological horizon to be received by an antipodal observer. Generically, this information transfer takes a scrambling time $t = H^{-1}\log(S_{\rm dS})$. We emphasize that this procedure relies crucially on selection of the Bunch-Davies vacuum state, interpreted as the thermofield double state that maximally entangles two antipodal static patches. The procedure also requires the presence of an (entangled) energy reservoir, created by the collection of Hawking modes from the cosmological horizon. We show how this procedure avoids a cloning paradox and comment on its implications.

Figures (7)

• Figure 1: Two antipodal static patch regions (shaded blue). The thermofield double state with Hilbert space ${\cal H}_{\rm TFD} = {\cal H}_N\otimes{\cal H}_S$ is constructed by maximally entangling the two static patches.
• Figure 2: De Sitter Penrose diagram and global lightcone coordinates. The two static patches are shaded blue.
• Figure 3: A pair of shockwaves in de Sitter space and a shifted lightray
• Figure 4: Quantum circuit corresponding to the Hayden-Preskill protocol. Figure from Hayden:2007cs.
• Figure 5: In the thermofield double state, for each mode there is a maximally entangled mirror mode across the horizon.