  The real part of pseudo entropy in conformal field theories is
holographically calculated by the area of some extremal spacelike surfaces in
the dual dS and AdS spacetimes. We show that the flat-space limit of these
curves in three dimensional (A)dS spacetimes is well-defined. We find that if
the length of the curves is calculated from the radial coordinate where the
retarded time is extremum, then after taking the flat-space limit, the
entanglement entropy of the dual theory of three-dimensional flat spacetime is
obtained. For dS spacetime, the radial coordinate corresponding to the extremum
of retarded time is located inside the cosmological horizon. Our results
suggest that on the field theory side, the entanglement entropy in the dual
theory of flat spacetimes should be obtained from the ultra-relativistic limit
of pseudo entropy in the dual CFT to (A)ds spacetimes.
