Inflationary multiverse framework, conditions, and forecasts

Le résumé fourni par la source

We present a comprehensive theoretical framework for the inflationary multiverse, covering the full dynamics of inflation, bubble nucleation, and the expected number of collisions from first principles. We derive the complete set of conditions that a single-field inflationary universe must satisfy to produce a realistic bubble-nucleation scenario, including the requirements for a false vacuum, a barrier, a true vacuum, and a slow-roll plateau that supports inflation. We formulate the exact Euclidean bounce action by solving the O(4)-symmetric field equations, and we evaluate the expected number of bubble collisions \(N_{\rm coll}\) within the FKNS parametrization. We then perform a Fisher matrix analysis to forecast the constraining power of current and future CMB experiments on the parameters of the model and on the derived quantities \(B\) and \(N_{\rm coll}\). We consider three scenarios: a pessimistic case corresponding to the Simons Observatory without delensing, a realistic case corresponding to Simons Observatory with delensing or a conservative CMB-S4 configuration, and an optimistic case corresponding to the combined performance of CMB-S4 and LiteBIRD. Our forecasts demonstrate that Stage-IV CMB experiments will dramatically reduce the uncertainties on both the potential parameters and the bubble-nucleation predictions, providing a clear pathway to test the multiverse paradigm. All conditions are formulated mathematically, and the numerical implementation is publicly available at \href{https://github.com/lontelis/Inflationary-multiverse-conditions-and-forecasts}{GitHub}. This work provides a complete, self-contained framework for connecting inflationary dynamics to observable signatures of bubble nucleation in the multiverse. The central result—the unique prediction for the number of bubble collisions—is presented in a companion letter. (This version (v2) finalizes the structurally independent implementation of the potential. The core mathematical framework and structural changes were completed on 17 August 2026 and are now fully incorporated. Version 1 remains available for historical reference.)

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