arXiv subjects

Jean-Luc Lehners

Publications and source records attributed to Jean-Luc Lehners.

At least 19 recordsLinked to original sources

arXiv2026

Birth of Inflationary Universes via Wineglass Wormholes and their No-Boundary Relatives

We study Euclidean wineglass wormholes, which mediate the nucleation of inflationary spacetimes from an existing spacetime with asymptotically flat or Anti-de Sitter regions. These wormholes are distinguished by the presence of a local maximum of the scale factor, which allows the analytically continued Lorentzian spacetime to expand after materialization. We present explicit numerical wormhole solutions supported either by an axionic field or a magnetic gauge field, in both cases in conjunction with a self-interacting scalar field. More exotic solutions, with multiple extrema of the scale factor, are also described. As we discovered recently, in the limit of small axionic or magnetic charge, wineglass wormhole solutions split into two separate geometries, one being the background spacetime and the other a disconnected no-boundary instanton. We study the associated topology changing transition in detail and provide an extensive discussion of both the properties and puzzles exhibited by this common family of wineglass/no-boundary instantons.

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arXiv2026

Quantum States Prepared by Wormholes: Long-Wavelength Deviations from Bunch-Davies

Wineglass wormholes mediate the nucleation of baby universes out of an asymptotically Anti-de Sitter or flat spacetime. Upon materialization, the new universe naturally undergoes an inflationary phase. Here we study the quantum state of tensor and probe scalar field fluctuations that these wormhole geometries prepare, finding that they reproduce the Bunch-Davies vacuum for short-wavelength modes but lead to deviations from Bunch-Davies on large scales. These deviations, which depend on the charge of the wormhole, cause a small shift as well as oscillations in the angular power spectrum generated by an ensuing inflationary phase, and thus provide a distinctive cosmological observable. The wormholes are supported by either axionic or magnetic charges. In the limit of vanishing charge, they undergo a topological transition after which they contain no-boundary instantons. We find that the small-charge limit suppresses deviations from the Bunch-Davies state for both scalar and tensor fluctuations, indicating that the topological transition is smooth.

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arXiv2026

Nucleating an Inflationary Universe: Euclidean Wormholes and their No-Boundary Limit

No-boundary instantons and Euclidean "wineglass" wormholes have both been proposed as providing suitable initial conditions for the current expanding phase of our universe, and in particular for providing conditions that are favorable to an inflationary phase. These finite action solutions have generally been regarded as unrelated, and enacting different scenarios - in one case the creation of spacetime from nothing, and in the other up-tunneling from a Euclidean Anti-de Sitter vacuum. By studying explicit solutions of both axionic and magnetic wineglass wormholes, we find that in the zero-charge limit the throat of the wormholes pinches off, leaving a no-boundary instanton that disconnects from the asymptotic Anti-de Sitter region. Thus wormholes and no-boundary instantons are part of a common family of Euclidean solutions. Along the way, we resolve the long-known puzzle that the action of wineglass wormholes can become negative. Moreover, small-charge wormholes lead to a longer inflationary phase than large-charge solutions, while no-boundary instantons dominate the probability distribution overall.

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arXiv2025

Delicate curvature bounces in the no-boundary wave function and in the late universe

Theoretical considerations motivate us to consider vacuum energy to be able to decay and to assume that the spatial geometry of the universe is closed. Combining both aspects leads to the possibility that the universe, or certain regions thereof, can collapse and subsequently undergo a curvature bounce. This may have occurred in the very early universe, in a pre-inflationary phase. We discuss the construction of the corresponding no-boundary instantons and show that they indeed reproduce a bouncing history of the universe, interestingly with a small and potentially observable departure from classicality during the contracting phase. Such an early bouncing history receives a large weighting and provides competition for a more standard inflationary branch of the wave function. Curvature bounces may also occur in the future. We discuss the conditions under which they may take place, allowing for density fluctuations in the matter distribution in the universe. Overall, we find that curvature bounces require a delicate combination of matter content and initial conditions to occur, though with significant consequences if these conditions are met.

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arXiv2024

Review of the No-Boundary Wave Function

When the universe is treated as a quantum system, it is described by a wave function. This wave function is a function not only of the matter fields, but also of spacetime. The no-boundary proposal is the idea that the wave function should be calculated by summing over geometries that have no boundary to the past, and over regular matter configurations on these geometries. Accordingly, the universe is finite, self-contained and the big bang singularity is avoided. Moreover, given a dynamical theory, the no-boundary proposal provides probabilities for various solutions of the theory. In this sense it provides a quantum theory of initial conditions. This review starts with a general overview of the framework of quantum cosmology, describing both the canonical and path integral approaches, and their interpretations. After recalling several heuristic motivations for the no-boundary proposal, its consequences are illustrated with simple examples, mainly in the context of cosmic inflation. We review how to include perturbations, assess the classicality of spacetime and how probabilities may be derived. A special emphasis is given to explicit implementations in minisuperspace, to observational consequences, and to the relationship of the no-boundary wave function with string theory. At each stage, the required analytic and numerical techniques are explained in detail, including the Picard-Lefschetz approach to oscillating integrals.

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arXiv2024

Stability of Axion-Dilaton Wormholes

We study the perturbative stability of Euclidean axion-dilaton wormholes that asymptotically approach flat space, both with a massless and a massive dilaton, and focussing on homogeneous perturbations. We find massless wormholes to always be perturbatively stable. The phenomenologically more relevant case of a massive dilaton presents us with a wide variety of wormhole solutions, depending on the dilaton coupling and mass, and on the axion charge. We find that the solutions with the smallest dilaton potential are perturbatively stable and dominant, even in cases where the wormhole solutions are not continuously connected to the massless case by decreasing the mass. For branches of solutions emanating from a bifurcation point, one side of the branch always contains a negative mode in its spectrum, rendering such solutions unstable. The existence of classes of perturbatively stable wormhole solutions with massive dilaton sharpens the puzzles associated with Euclidean wormholes.

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arXiv2024

NUTs, Bolts and Stokes Phenomena in the No-Boundary Wave Function

In this note, we revisit and extend the analysis of the no-boundary wave function for the minisuperspace model in which the universe is described by a biaxial Bianchi IX metric. As matter content, we simply assume a positive cosmological constant. We find that two Stokes phenomena occur, at large squashing parameters of the spatial section of the universe. These Stokes phenomena eliminate potentially dominant Taub-Bolt-de Sitter saddle point geometries and are crucial for the consistency of the model. They also imply that phase transitions occur at certain levels of squashing, where NUT and Bolt saddle points exchange dominance.

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arXiv2024

A small Universe

Many cosmological models assume or imply that the total size of the universe is very large, perhaps even infinite. Here we argue instead that the universe might be comparatively small, in fact not much larger than the currently observed size. A concrete implementation of this idea is provided by the no-boundary proposal, in combination with a plateau-shaped inflationary potential. In this model, opposing effects of the weighting of the wave function and of the criterion of allowability of the geometries conspire to favour small universes. We point out that a small size of the universe also fits well with swampland conjectures, and we comment on the relation with the dark dimension scenario.

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arXiv2023

Higher-Order Gravity, Finite Action, and a Safe Beginning for the Universe

General relativity allows for inhomogeneous and anisotropic universes with finite action. By contrast, in quadratic gravity such solutions obtain infinite action and are thus eliminated. What remains are homogeneous and isotropic solutions undergoing accelerated expansion, thereby automatically inducing an early inflationary phase. In this manner, semi-classical consistency may explain some of the basic, coarse-grained features of the early universe. This includes suitable initial conditions for the second law of thermodynamics, in the spirit of the Weyl curvature hypothesis. We note that quadratic gravity is a renormalisable theory and may admit an asymptotically safe regime at high energies, rendering the theory trustworthy to high energies. We also comment on theories containing curvature terms up to infinite derivative order, and on the contrast with no-boundary initial conditions.

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arXiv2023

A Zoo of Axionic Wormholes

As was discovered some time ago by Giddings and Strominger (GS), an axion can support a wormhole geometry in the presence of a massless dilaton, as long as the dilaton coupling remains below a critical value. We find that when the dilaton becomes massive, the set of solutions is vastly increased: not only do solutions exist above the critical value of the coupling, but new branches of solutions with several minima in the geometry also appear. All of these generalised GS-like solutions possess the property that, when analytically continued, they lead to a contracting baby universe. We show that in addition there exist families of solutions which, upon analytic continuation, lead to expanding baby universes. A curious property of axion-dilaton wormhole families is that their Euclidean action often decreases when the solutions acquire additional oscillations in the fields. When we replace the dilaton by an ordinary scalar field with a double well potential, we find analogous wormhole families leading to expanding baby universes. This time the Euclidean action has the expected behaviour of increasing with the number of oscillations in the fields, although it also contains a puzzling aspect in that some solutions possess a negative action.

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arXiv2022

Allowable Complex Scalars from Kaluza-Klein Compactifications and Metric Rescalings

Recently there have been discussions about which complex metrics should be allowable in quantum gravity. These discussions assumed that the matter fields were real valued. We make the observation that for compactified solutions it makes sense to demand convergence of the theory's path integral in the higher-dimensional parent theory. Upon compactification this allows for more general matter configurations in the lower-dimensional theory, in particular it allows for complex scalar fields, with a bound on their imaginary parts. Similar considerations apply to metric rescalings in the presence of higher curvature corrections. We illustrate this effect with the example of the no--boundary proposal, in which scalar fields are typically required to take complex values. We find that complex no-boundary solutions exist, and satisfy the derived bound, if the potential is sufficiently flat. For instance, for a compactification from $D$ dimensions, the bound on the imaginary part $\textrm{Im}\,(ϕ)$ of the internal volume modulus reads $V_{,ϕ}/V < \sqrt{\frac{D-4}{D-2}}/3\sqrt{2}.$ This leads to a mild tension with swampland conjectures.

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arXiv2022

How to Create Universes with Internal Flux

String compactifications typically require fluxes, for example in order to stabilise moduli. Such fluxes, when they thread internal dimensions, are topological in nature and take on quantised values. This poses the puzzle as to how they could arise in the early universe, as they cannot be turned on incrementally. Working with string inspired models in $6$ and $8$ dimensions, we show that there exist no-boundary solutions in which internal fluxes are present from the creation of the universe onwards. The no-boundary proposal can thus explain the origin of fluxes in a Kaluza-Klein context. In fact, it acts as a selection principle since no-boundary solutions are only found to exist when the fluxes have the right magnitude to lead to an effective potential that is positive and flat enough for accelerated expansion. Within the range of selected fluxes, the no-boundary wave function assigns higher probability to smaller values of flux. Our models illustrate how cosmology can act as a filter on a landscape of possible higher-dimensional solutions.

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arXiv2022

Uses of Complex Metrics in Cosmology

Complex metrics are a double-edged sword: they allow one to replace singular spacetimes, such as those containing a big bang, with regular metrics, yet they can also describe unphysical solutions in which quantum transitions may be more probable than ordinary classical evolution. In the cosmological context, we investigate a criterion proposed by Witten (based on works of Kontsevich & Segal and of Louko & Sorkin) to decide whether a complex metric is allowable or not. Because of the freedom to deform complex metrics using Cauchy's theorem, deciding whether a metric is allowable in general requires solving a complicated optimisation problem. We describe a method that allows one to quickly determine the allowability of minisuperspace metrics. This enables us to study the off-shell structure of minisuperspace path integrals, which we investigate for various boundary conditions. Classical transitions always reside on the boundary of the domain of allowable metrics, and care must be taken in defining appropriate integration contours for the corresponding gravitational path integral. Perhaps more surprisingly, we find that proposed quantum (`tunnelling') transitions from a contracting to an expanding universe violate the allowability criterion and may thus be unphysical. No-boundary solutions, by contrast, are found to be allowable, and moreover we demonstrate that with an initial momentum condition an integration contour over allowable metrics may be explicitly described in arbitrary spacetime dimensions.

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arXiv2022

No-boundary prescriptions in Lorentzian quantum cosmology

We analyse the impact of various boundary conditions on the (minisuperspace) Lorentzian gravitational path integral. In particular we assess the implications for the Hartle-Hawking no-boundary wavefunction. It was shown recently that when this proposal is defined as a sum over compact metrics, problems arise with the stability of fluctuations. These difficulties can be overcome by an especially simple implementation of the no-boundary idea: namely to take the Einstein-Hilbert action at face value while adding no boundary term. This prescription simultaneously imposes an initial Neumann boundary condition for the scale factor of the universe and, for a Bianchi IX spacetime, Dirichlet conditions for the anisotropies. Another way to implement the no-boundary wavefunction is to use Robin boundary conditions. A sub-class of Robin conditions allows one to specify the Hubble rate on the boundary hypersurface, and we highlight the surprising aspect that specifying the final Hubble rate (rather than the final size of the universe) significantly alters the off-shell structure of the path integral. The conclusion of our investigations is that all current working examples of the no-boundary wavefunction force one to abandon the notion of a sum over compact and regular geometries, and point to the importance of an initial Euclidean momentum.

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arXiv2022

Allowable complex metrics in minisuperspace quantum cosmology

Kontsevich and Segal (K-S) have proposed a criterion to determine which complex metrics should be allowed, based on the requirement that quantum field theories may consistently be defined on these metrics, and Witten has recently suggested that their proposal should also apply to gravity. We explore this criterion in the context of gravitational path integrals, in simple minisuperspace models, specifically considering de Sitter (dS), no-boundary and Anti-de Sitter (AdS) examples. These simple examples allow us to gain some understanding of the off-shell structure of gravitational path integrals. In all cases, we find that the saddle points of the integral lie right at the edge of the allowable domain of metrics, even when the saddle points are complex or Euclidean. Moreover the Lefschetz thimbles, in particular the steepest descent contours for the lapse integral, are cut off as they intrude into the domain of non-allowable metrics. In the AdS case, the implied restriction on the integration contour is found to have a simple physical interpretation. In the dS case, the lapse integral is forced to become asymptotically Euclidean. We also point out that the K-S criterion provides a reason, in the context of the no-boundary proposal, for why scalar fields would start their evolution at local extrema of their potential.

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arXiv2022

Scalar Lumps with Two Horizons

We study generalisations of the Schwarzschild-de Sitter solution in the presence of a scalar field with a potential barrier. These static, spherically symmetric solutions have two horizons, in between which the scalar interpolates at least once across the potential barrier, thus developing a lump. In part, we recover solutions discussed earlier in the literature and for those we clarify their properties. But we also find a new class of solutions in which the scalar lump curves the spacetime sufficiently strongly so as to change the nature of the erstwhile cosmological horizon into an additional trapped horizon, resulting in a scalar lump surrounded by two black holes. These new solutions appear in a wide range of the parameter space of the potential. We also discuss (challenges for) the application of all of these solutions to black hole seeded vacuum decay.

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arXiv2021

Revisiting the no-boundary proposal with a scalar field

Recent works have suggested that the no-boundary proposal should be defined as a sum over regular, not necessarily compact, metrics. We show that such a prescription can be implemented in the presence of a scalar field. For concreteness, we consider the model of Garay et al., in which the potential is a sum of exponentials, and which lends itself to an analytical treatment. Compared to the earlier implementation, we find that saddle points with unstable fluctuations can be eliminated by imposition of an appropriate regularity condition. This leads to the appearance of additional saddle points, corresponding to unclosed geometries. We argue that such saddles will occur generically, though we also find in our example that they are subdominant to the closed, Hartle-Hawking, saddle points. When the potential is positive, classical spacetime is only predicted for inflationary histories. When the potential is negative, we recover the AdS gravitational path integral, with a stable scalar field included. One puzzle that we find is that in general the path integral must be restricted to sum only over specific, discrete and late time dependent initial values of the scalar field. Only when the scalar is required to take real values is this puzzle eliminated, a situation that moreover leads to advantageous phenomenological characteristics.

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arXiv2021

The Wave Function of Simple Universes, Analytically Continued From Negative to Positive Potentials

We elaborate on the correspondence between the canonical partition function in asymptotically AdS universes and the no-boundary proposal for positive vacuum energy. For the case of a pure cosmological constant, the analytic continuation of the AdS partition function is seen to define the no-boundary wave function (in dS) uniquely in the simplest minisuperspace model. A consideration of the AdS gravitational path integral implies that on the dS side, saddle points with Hawking-Moss/Coleman-De Luccia-type tunnelling geometries are irrelevant. This implies that simple topology changing geometries do not contribute to the nucleation of the universe. The analytic AdS/dS equivalence holds up once tensor fluctuations are added. It also works, at the level of the saddle point approximation, when a scalar field with a mass term is included, though in the latter case, it is the mass that must be analytically continued. Our results illustrate the emergence of time from space by means of a Stokes phenomenon, in the case of positive vacuum energy. Furthermore, we arrive at a new characterisation of the no-boundary condition, namely that there should be no momentum flux at the nucleation of the universe.

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