The holographic $T\bar{T}$ deformation of the entanglement entropy in (A)dS$_3$/CFT$_2$

In recent years, the holographic duality between $T\bar{T}$-deformed conformal field theory (CFT) and Anti-de Sitter (AdS) space with finite radial truncation has received significant attention. The study of $T\bar{T}$ deformation within the framework of de Sitter (dS)/CFT duality has also progressed. This paper shows that the trace flow equation in dS spacetime can be analytically extended from its AdS counterpart through double Wick rotations. Additionally, we generalize the replica sphere method in both AdS and dS holography to derive a general expression for the entanglement entropy of arbitrary single spatial intervals. For both finite size and finite temperature systems, we obtain the entanglement entropy corrections due to $T\bar{T}$ deformation. Finally, using strong subadditivity and boosted strong subadditivity, we show that the dual field theory on the timelike boundary is non-local in dS holography.