A UV-complete, swampland-compatible multiverse: eternal inflation, realistic tunneling rates, and the minimum inflationary duration in an actual landscape

D'Agnolo, Mangini, Rigo and Wang showed at the effective-field-theory level that a multiverse scanning the cosmological constant and the weak scale can be populated by eternal inflation on steep potentials with sub-Planckian field excursions, in apparent compatibility with the distance and refined de Sitter swampland conjectures, and estimated that only about one hundred e-folds of inflation may suffice when de Sitter minima are allowed. Their construction, however, is a hilltop toy model whose last 60 e-folds must be supplied by a separate sector, with no UV-complete embedding, no computation of tunneling rates or volume fractions in a realistic landscape, and only toy-model support for the e-fold estimate. The open problem is to elevate this demonstration to a unified, UV-complete construction of a swampland-compatible multiverse with quantifiable population dynamics: a single controlled quantum-gravity model that produces the eternal (or sufficiently long) inflationary epoch, the observed last 60 e-folds, and the upward-tunneling rates and volume fractions that establish the multiverse is actually populated.

Background

The swampland program conjectures which low-energy effective field theories (EFTs) can be consistently coupled to gravity, i.e. UV-completed in a theory of quantum gravity such as string theory, as opposed to lying in the 'swampland'. Two conjectures are central here. The distance conjecture (Ooguri and Vafa) states that as a scalar field excursion in field space grows beyond the Planck scale $M_{\rm Pl}$, an infinite tower of states becomes light and the EFT breaks down; viable theories should therefore admit inflation with sub-Planckian field displacement. The refined de Sitter (dS) conjecture (Garg and Krishnan; Ooguri, Palti, Shiu and Vafa) states that in a consistent quantum gravity the scalar potential satisfies $M_{\rm Pl}|\nabla V|/V \geq c$ with $c$ of order one, or else $V < 0$ — in particular generic metastable de Sitter vacua (positive-energy stationary points) are disallowed. Together these conjectures appear to tension with slow-roll inflation (cosmic microwave background (CMB) data — the relic radiation from the early universe — require an almost flat potential) and, more drastically, with the multiverse: the anthropic explanation of the small observed cosmological constant (Weinberg's argument that only vacua with small enough vacuum energy allow galaxies, and hence observers, to form) requires a landscape of many vacua with different vacuum energies, populated by a long period of eternal inflation.

Eternal inflation is a regime in which quantum fluctuations of the inflaton (the scalar field whose potential energy drives inflation) dominate over its classical rolling, so that inflation never ends globally: thermalized 'pocket universes' form inside bubbles nucleated by Coleman–De Luccia (CDL) tunneling — quantum tunneling between vacua mediated by a bounce instanton — or by Hawking–Moss jumps over a potential barrier, while inflation continues outside. Ordinarily the landscape is assumed to contain de Sitter minima. Earlier work argued that eternal inflation is excluded by the swampland conjectures: Kinney showed a tuned hilltop eternal-inflation model is incompatible with the refined dS conjecture; Brahma and Shandera argued stochastic eternal inflation lies in the swampland; Wang, Brandenberger and Heisenberg derived entropy-bound obstructions; while Dimopoulos, Matsui and Takahashi, and Blanco-Pillado, Deng and Vilenkin found loopholes at the price of trans-Planckian excursions or landscape tuning.

Against this background, D'Agnolo, Mangini, Rigo and Wang ('A Multiverse Outside of the Swampland', Phys. Rev. D 110 (2024) 055007) constructed the leading counterexample: a simple hilltop model of eternal inflation on a steep potential ($M_{\rm Pl}|\nabla V|/V > 1$, no dS minima) with sub-Planckian field excursion, in which upward tunneling from the true (lower-energy) vacuum to a higher-energy false vacuum nucleates false-vacuum bubbles that pinch off into baby universes, populating a landscape of Minkowski (zero vacuum energy) and anti-de Sitter (AdS, negative vacuum energy) vacua that scans the cosmological constant and the weak scale. For the last 60 e-folds needed to describe our Universe (the model's own perturbations would overproduce the CMB quadrupole), they invoke a second sector, including a warm-inflation option: inflation with a dissipation term $\Upsilon$ from coupling the inflaton to a thermal bath, which adds friction so a steep potential can still inflate. Warm inflation, however, faces a generic obstruction (Yokoyama and Linde): the same coupling that generates thermal friction also generates large radiative corrections to the inflaton mass that steepen the potential; only special protected couplings such as the axion-like $\phi F\tilde F$ coupling (minimal warm inflation of Berghaus, Graham and Kaplan, and its heavy-QCD-axion variant of Berghaus, Forslund and Guevarra) evade it, and those models resist UV completion because the inflaton is simultaneously a compact field (in the coupling) and a non-compact one (in the potential). Finally, relaxing the no-dS-minima assumption — in that second branch they allow de Sitter minima in the landscape and drop the refined de Sitter bound as a working hypothesis — they estimated that a 'standard' multiverse can be populated by CDL transitions in only $\mathcal{O}(100)$ e-folds of inflation — challenging the lore that a CC-explaining multiverse requires eternal inflation — but this estimate rests on toy assumptions about the distribution of vacua and bubble dynamics. The authors explicitly set aside the measure problem of eternal inflation (how to define probabilities in an eternally inflating spacetime) and Boltzmann-brain paradoxes (the concern that in an eternally inflating spacetime, rare fluctuation-assembled observers would vastly outnumber ordinary ones); these are not part of the present question.

Problem Statement

The common objective is to determine whether the EFT-level demonstration of D'Agnolo, Mangini, Rigo and Wang — that a multiverse scanning the cosmological constant and the weak scale is compatible with the distance and refined de Sitter swampland conjectures — can be realized in a unified, UV-complete theory of quantum gravity with quantifiable population dynamics. Concretely, construct or rule out a single controlled UV-complete model (for example a string compactification with a specified scheme for stabilizing its moduli — the light scalar fields parameterizing the compactification's internal geometry, which must be held fixed for the low-energy potential to be controlled) that satisfies all of the following linked requirements: (i) it contains an epoch of eternal inflation on a steep potential obeying $M_{\rm Pl}|\nabla V|/V \geq c$ with $c$ of order one, with sub-Planckian field excursion and without the EFT breaking down — or, in the alternative branch considered by the source paper, in which de Sitter minima are allowed and the refined de Sitter bound is dropped for that branch, an inflationary epoch of the minimum duration actually required to populate the landscape; (ii) the same theory supplies the last 60 e-folds of inflation compatible with CMB observations (spectral index $n_s$, scalar amplitude $A_s$, and the observational upper bound on the tensor-to-scalar ratio $r$) — these e-folds must be produced within the single UV-complete model constructed under (i), whether by the same field that drives the epoch of (i) or by additional fields or sectors belonging to that model, and must not be delegated to a separate theory or to a sector outside that model; (iii) the Coleman-De Luccia / Hawking-Moss tunneling rates that populate the landscape in the chosen branch, in the direction appropriate to that branch (upward transitions from the true vacuum to higher-energy vacua in the eternal-inflation branch; downward transitions from the de Sitter vacuum in the finite-duration branch), together with the branch-appropriate population quantity — coarse-grained volume fractions of the populated landscape in the eternal-inflation branch, and the number of bubbles nucleated within the inflating region in the finite-duration branch — are computed in that realistic landscape, establishing that the multiverse is actually populated; and (iv) the number of e-folds needed to populate the landscape is determined for the realistic vacuum distribution and bubble dynamics, testing whether the $\mathcal{O}(100)$-e-folds estimate survives. A construction may realize requirements (i)-(iv) using either branch of (i), with (ii)-(iv) delivered within that branch, whereas a refutation must exclude a model in both branches of (i). The measure problem of eternal inflation is not part of the question and need not be solved: the rates requested are the physical nucleation rates, and the volume fractions are coarse-grained volume fractions of the landscape dynamics evaluated with respect to a slicing, regulator or coarse-graining convention that is stated explicitly. Since, as the source paper notes, no gauge-invariant measure can be defined for observables throughout an eternally inflating multiverse, a population claim in the eternal-inflation branch is well defined only relative to the convention so declared, whereas in the finite-duration branch the relevant quantity is the number of bubbles nucleated within the inflating region, which requires no measure.

References

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