A Half de Sitter Holography

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.