Euclidean wormholes of the 'wine glass' type are studied, mediating the nucleation of inflationary spacetimes from an existing universe with asymptotically flat or anti-de Sitter regions. Such wormholes feature a local maximum of the scale factor, which after analytic continuation to Lorentzian metric ensures the expansion of the newborn universe. Explicit numerical solutions are presented, supported by an axionic or magnetic gauge field along with a self-interacting scalar; exotic solutions with several extrema of the scale factor are also described. In the limit of small axionic or magnetic charge, the solutions split into two separate geometries: a background spacetime and a disconnected no-boundary instanton. The corresponding topology-changing transition is investigated in detail, discussing properties and paradoxes typical of this general family of 'wine glass'/no-boundary instantons.
Despite the success of inflation proposed by Guth, how it actually started remains a puzzle. Classical evolution runs into the Big Bang singularity. Quantum scenarios involve either tunneling from an already existing universe (wormholes) or birth from 'nothing' (Hawking and Hartle). These approaches have long been considered independent, but new work demonstrates their deep connection.
The authors numerically solved Euclidean Einstein equations with matter in the form of an axion field or magnetic charge and a self-interacting scalar with a potential featuring a maximum and minimum. Using the shooting method, they tuned initial conditions to ensure an asymptotically flat or AdS space on one end and a local maximum of the scale factor on the other.
Wormholes were found with a distinctive scale factor shape: 'rim' (local maximum), 'stem' (minimum), and 'base' (asymptotics). The transition in the stem region features extreme spacetime curvature. For small axion (or magnetic) charges, the scalar field starts near the top of the potential, giving prolonged inflation after analytic continuation to Lorentzian signature. The Euclidean action (weight in the Feynman integral) decreases with charge, so universes with longer inflation are more probable. In the limit of vanishing charge, the stem disappears and the geometry splits into two disconnected parts: the no-boundary instanton (de Sitter sphere) and the background space. The weighting coefficient smoothly transitions to -S ≈ 118.4 for the inflationary vacuum at the top of the potential. Exotic solutions with multiple bridges or crossing several barriers were also found, but they are suppressed.
This discovery blurs the line between two paradigms of quantum cosmology: wormholes and the no-boundary state of Hawking. It hints at the possibility of topology change in quantum gravity and supports the idea that different topologies contribute to the wave function of the Universe. Moreover, it naturally provides initial conditions for inflation.
Future research may include stability analysis of these solutions, searching for complex (fuzzy) analogs, and exploring their role in determining the integration contour for the gravitational path integral. It is also important to understand how these configurations fit into cosmological measure theory and resolve the problem of initial probabilities.
The work impacts inflationary cosmology, string theory (via AdS/CFT correspondence), and the interpretation of cosmic microwave background data, which constrains the scale of inflation.
Next steps include calculating the perturbation spectrum born in such scenarios and checking against the Kontsevich–Segal–Witten admissibility criterion.
Connection to unsolved problems: the initial conditions problem for inflation, the measure problem in eternal inflation, and the factorization paradox in AdS/CFT.
🎯 The scale factor shape of these wormholes resembles a wine glass: a wide bowl (future universe), a narrowing stem (throat), and a base (asymptotics). Hence the poetic name.
🎬 In the movie 'Interstellar,' wormholes serve as passages between galaxies, while here they act as cradles for entire universes—albeit only at the quantum level.