Bag-of-gold spacetimes, Euclidean wormholes, and inflation from domain walls in AdS/CFT

We use Euclidean path integrals to explore the set of bulk asymptotically AdS spacetimes with good CFT duals. We consider simple bottom-up models of bulk physics defined by Einstein-Hilbert gravity coupled to thin domain walls and restrict to solutions with spherical symmetry. The cosmological constant is allowed to change across the domain wall, modeling more complicated Einstein-scalar systems where the scalar potential has multiple minima. In particular, the cosmological constant can become positive in the interior. However, in the above context, we show that inflating bubbles are never produced by smooth Euclidean saddles to asymptotically AdS path integrals. The obstacle is a direct parallel to the well-known obstruction to creating inflating universes by tunneling from flat space. In contrast, we do find good saddles that create so-called "bag-of-gold" geometries which, in addition to their single asymptotic region, also have an additional large semi-classical region located behind both past and future event horizons. Furthermore, without fine-tuning model parameters, using multiple domain walls we find Euclidean geometries that create arbitrarily large bags-of-gold inside a black hole of fixed horizon size, and thus at fixed Bekenstein-Hawking entropy. Indeed, with our symmetries and in our class of models, such solutions provide the unique semi-classical saddle for appropriately designed (microcanonical) path integrals. This strengthens a classic tension between such spacetimes and the CFT density of states, similar to that in the black hole information problem.