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

TL;DR

Facing the de Sitter entropy puzzle, this work analyzes bra-ket wormholes and their non-factorizing contributions to two-point correlators in a JT gravity setup with scalar QFT. It introduces two observables based on k_max and k_min to diagnose late-time wormhole effects and constructs an effective bra-ket wormhole by tracing over an unobservable universe, uncovering a phase transition to wormhole dominance that yields ramp-plateau correlation behavior. The results reveal low-k enhancement and scrambling-like dynamics, with a fast scrambling timescale emerging from a competition between mode counting and topological suppression, offering a potential avenue to reconcile finite entropy with cosmological correlations. Stabilization of wormholes remains an open requirement to fully interpret entropy and chaotic properties of de Sitter space.

Abstract

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.

Figures (14)

• Figure 1: dS prepares a quantum state (of the scalar field) on its spatial boundary $\Sigma$, reheating surface, including effects from higher-topology wormholes. The state is then observable in the flat space afterwards without gravity. Two notions of time, $k_{\rm max}$ and $k_{\rm min}$, define two observables.
• Figure 2: (Left:) HH no-boundary saddle in Eq. (\ref{['eq:HHsaddle']}). (Right:) Its contribution to the density matrix in Fig. \ref{['fig:SchematicDM']} by a single path integral.
• Figure 3: 2-boundary wormhole saddle at NLO in Eq. (\ref{['eq:bkwh0']}), which is a building block of the bra-ket wormhole in Fig. \ref{['fig:SchematicDM']} and Sec. \ref{['sec:trace_univ']}. This by itself can only be a ket-ket or bra-bra wormhole because continuity of fields in the throat disallows proper boundary conditions for bra-ket wormholes (Sec. \ref{['sec:naiveWH']}).
• Figure 4: Gravitational path integral calculation of density matrix, in the field basis. The leading contribution is a product of HH states, while the NLO contribution is the effective bra-ket wormhole, which is obtained by joining two 2-boundary wormholes in Fig. \ref{['fig:bkwh0']} and tracing out unobservable separate universe (denoted with $\phi_2$); see Sec. \ref{['sec:trace_univ']}.
• Figure 5: The scaling relation between free parameters of the model, $\{ S_{\rm dS}, \tau_0, k_{\rm max} \}$, using $k_{\rm max}^c$ as a function of $\tau_0$ for two choices of $S_{\rm dS}=76$(solid), 760(dashed). Shown numerical values are for $S_{\rm dS}=76$, while the result of $S_{\rm dS}=760$ is rescaled by Eq. (\ref{['eq:scaling']}) with $c=1/10$, and they overlap very well. Furthermore, the scaling allows to categorize the whole parameter space into three regimes separated by vertical lines. The scrambling timescale turns out to be relevant to the bra-ket wormhole, but the exact location of a theory depends on a true stabilization mechanism. The benchmark parameter in the scrambling regime is marked as a cross.