Holographic complexity of conformal fields in global de Sitter spacetime

We compute the holographic complexity of conformal quantum fields in rigid global de Sitter spacetime (dS$_{d}$) using the volume and action prescriptions. First we consider AdS$_{d+1}$ spacetime in global dS$_{d}$ foliations, and compute the complexity of the CFT supported on the global dS$_{d}$ conformal boundary. Next, we consider CFT supported on a global dS$_d$ (UV) brane embedded in AdS$_{d+1}$ spacetime, and compute the holographic complexity in this brane set up. We compare and contrast the results in the two cases, as well as with related results in the literature obtained in alternative holographic set ups involving patches of de Sitter spacetime covered by static coordinates or conformal (Poincar\'e) coordinates.