de Sitter entropy as entanglement
K. Narayan
TL;DR
This essay explores whether de Sitter entropy can be understood as entanglement within a dS/CFT framework. It argues that connected timelike codim-2 extremal surfaces between the future and past boundaries in de Sitter space yield an area scaling that mirrors $dS_4$ entropy, supporting an interpretation in which entropy arises from entanglement between two CFT copies living on $I^+$ and $I^-$. By examining ghost-like CFTs and correlated ghost-spin models, it contends that a two-copy entangled state (a thermofield double) of Euclidean boundary theories can produce positive norm and entanglement, providing a microscopic route to the entropy. The proposed picture links holographic extremal surfaces, ghost-CFTs, and entanglement as a potential microscopic account of cosmological horizon entropy, while noting caveats related to regions behind horizons and interior operators.
Abstract
We describe connected timelike codim-2 extremal surfaces stretching between the future and the past boundaries in the static patch coordinatization of de Sitter space. These are analogous to rotated versions of certain surfaces in the $AdS$ black hole. The existence of these surfaces via the $dS/CFT$ framework suggests the speculation that $dS_4$ is dual to two copies of ghost-like CFTs in a thermofield-double-type entangled state. In studies of entanglement in ghost systems and "ghost-spin" chains, we show that similar entangled states in two copies of ghost-spin ensembles always have positive norm and positive entanglement.