An AS${}^2$ Menagerie

TL;DR

This work expands the AS^2 program by constructing a large family of exact $AdS_3$ gravity solutions with heavy particles, obtained via gluing $AdS_3$ tubes to a parent Euclidean wormhole, to realize cosmologies that can be nearly homogeneous and isotropic. It establishes a necessary condition for a cosmological saddle to dominate the Euclidean path integral and demonstrates that the original AS^2 construction typically fails to meet this criterion, favoring alternative saddles in the large-$c$ limit. The authors also explore scenarios that could promote cosmological dominance, such as ensembles or many connected tubes, and discuss multi-universe saddles and implications for thin-shell black hole states and potential connections to baryon asymmetry. Overall, the paper clarifies when a closed-universe cosmology can be the dominant gravitational saddle and maps out a rich landscape of generalized AS^2 geometries and their holographic interpretations.

Abstract

We construct a large number of exact solutions of three-dimensional gravity with heavy matter particles that generalize the construction of Antonini, Sasieta, and Swingle (AS${}^2$), argued to define CFT states dual to a spacetime with a closed baby universe cosmology. Our construction starts with an arbitrary heavy-particle closed universe cosmology of the type constructed in arXiv:2503.12227, and via a gluing procedure adds an arbitrary number of AdS tubes connecting the past and future conformal boundaries of the associated Euclidean wormhole solution. With our construction, it is straightforward to produce examples where the cosmology is approximately homogeneous and isotropic. We describe a necessary condition for the cosmological wormhole saddle to dominate the Euclidean path integral with the specified boundary conditions. We argue that the original AS${}^2$ construction usually does not meet this condition, and describe alternative saddles that are likely to dominate. We discuss various possibilities for how the cosmological saddle might be made to dominate in our generalized construction.

Figures (19)

• Figure 1: Left: A Euclidean wormhole supported by matter particles corresponding to operator insertions; the Lorentzian continuation is a closed universe big-bang / big-crunch cosmology. Right: via surgery, we can add arbitrary numbers of AdS cylinders connecting the past and future conformal boundaries. These may include some of the matter particles (removing the portion of the boundary that contained the corresponding operator insertion). The Lorentzian continuation now contains the cosmology and a number of asymptotically AdS spacetimes, some containing partner particles entangled with particles in the cosmology.
• Figure 2: Left: a geodesic polygon in $H^2$. Right: Polygons with matching side lengths can be glued together smoothly, with possible conical defects at the vertices.
• Figure 3: Regions adjacent to a conical defect (red) can be represented as geodesic prisms in FRW-coordinates. Note that this picture is not the usual AdS cylinder with time-translation symmetry; the conformal boundary is at $u = \pm \infty$ in these coordinates.
• Figure 4: Each hyperbolic polygon $P$ in the Poincaré disk can be extended to a time reflection symmetric region $V_P$ of ${\rm AdS}_3$ bounded by geodesic surfaces. In the coordinates \ref{['cylinder']}, if the center of the hyperbolic disk $\tau=0$ is an interior point of the polygon, $V_P$ contains the two asymptotic regions $\tau = \pm \infty$. We refer to such a $V_P$ as a chewed AdS${}_3$.
• Figure 5: Each gluing of hyperbolic polygons to form a closed surface can be associated with a gluing of chewed AdS spaces to describe a wormhole geometry.