Holographic entanglement entropy in the FLRW universe

A bstract We compute the holographic entanglement entropy via the Ryu-Takayanagi prescription in the three-dimensional Friedmann-Lemaître-Robertson-Walker universe. We consider two types of holographic scenarios analogous to the static patch holography and half de Sitter holography, in which the holographic boundary is timelike and placed in the bulk. We find in general that strong subadditivity can be satisfied only in the former scenario, and, in addition, the holographic boundary must lie within the apparent horizon. Also, for the universe filled with an ideal fluid with constant equation of state w < –1, the condition is sharpened as that the holographic boundary must lie within the event horizon instead. These constraints provide necessary conditions for the dual quantum field theory to be standard and compatible with strong subadditivity.