Two-point correlators in de Sitter-prepared states with bra-ket wormholes

Motivated by the finiteness of de Sitter (dS) horizon entropy, we study how "bra-ket wormholes" modify correlation functions in gravitationally prepared states. Euclidean wormhole saddles in gravitational path integrals can generate non-factorizing contributions to correlation functions, as in replica-wormhole explanation of the Page curve and bra-ket-wormhole restoration of strong subadditivity. By defining 'time' variables and computing observables in a flat region attached to the dS boundary, we evaluate bra-ket wormhole contributions to scalar two-point functions and find late-time transitions in the dominant saddle, accompanied by the ramp-and-plateau behavior of correlations and the characteristic timescale comparable to the fast scrambling. Each observable is consistent with `complementarity', in the sense that wormhole effects are distinguishable only at late respective times. Consistencies are based upon the interplay of (i) inflationary horizon exit and re-entry, (ii) enhancement of correlations at small comoving momentum by wormhole contributions, (iii) a competition between mode counting and topological suppression that drives a transition to wormhole dominance, which naturally yields the fast scrambling timescale, and (iv) irreducible errors by cosmic variance in early CMB-like observations. To clearly interpret in terms of entropy and chaotic nature of dS, one needs a more complete mechanism of wormhole stabilization.