arXiv subjects

Jean-Luc Lehners

Publications and source records attributed to Jean-Luc Lehners.

At least 37 records · Page 2Linked to original sources

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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arXiv2021

Scalar lumps with a horizon

We study a self-interacting scalar field theory coupled to gravity and are interested in spherically symmetric solutions with a regular origin surrounded by a horizon. For a scalar potential containing a barrier, and using the most general spherically symmetric ansatz, we show that in addition to the known static, oscillating solutions discussed earlier in the literature there exist new classes of solutions which appear in the strong field case. For these solutions the spatial sphere shrinks either beyond the horizon, implying a collapsing universe outside of the cosmological horizon, or it shrinks already inside of the horizon, implying the existence of a black hole surrounding the scalar lump in all directions. Crucial for the existence of all such solutions is the presence of a scalar field potential with a barrier that satisfies the swampland conjectures.

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arXiv2021

Cosmological consequences of a principle of finite amplitudes

Over 30 years ago, Barrow & Tipler proposed the principle according to which the action integrated over the entire 4-manifold describing the universe should be finite. Here we explore the cosmological consequences of a related criterion, namely that semi-classical transition amplitudes from the early universe up to current field values should be well defined. On a classical level, our criterion is weaker than the Barrow-Tipler principle, but it has the advantage of being sensitive to quantum effects. We find significant consequences for early universe models, in particular: eternal inflation and strictly cyclic universes are ruled out. Within general relativity, the first phase of evolution cannot be inflationary, and it can be ekpyrotic only if the scalar field potential is trustworthy over an infinite field range. Quadratic gravity eliminates all non-accelerating backgrounds near a putative big bang (thus imposing favourable initial conditions for inflation), while the expected infinite series of higher-curvature quantum corrections eliminates Lorentzian big bang spacetimes altogether. The scenarios that work best with the principle of finite amplitudes are the no-boundary proposal, which gives finite amplitudes in all dynamical theories that we have studied, and string-inspired loitering phases. We also comment on the relationship of our proposal to the swampland conjectures.

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arXiv2021

Quantum Circuit Complexity of Primordial Perturbations

We study the quantum circuit complexity of cosmological perturbations in different models of the early universe. A natural measure for the complexity of cosmological perturbations is based on the symplectic group, allowing us to identify complexity with geodesics in the hyperbolic plane. We investigate the complexity of both the mode functions and the physical perturbations, arguing that the latter often provides a more insightful description of the physics involved. In all models the total complexity reached is rather large. Inflationary perturbations may be represented by a comparatively simple quantum circuit, while the perturbations during a matter-dominated contracting phase present the most rapid growth in complexity. Ekpyrotic perturbations reside in the middle and are distinguished by the smallest growth of complexity before horizon exit. Our analysis serves to highlight how different cosmological models achieve the same end result for the perturbations via different routes and how all models show a pronounced sensitivity to initial conditions.

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arXiv2021

No-boundary solutions are robust to quantum gravity corrections

The no-boundary proposal is a theory of the initial conditions of the universe formulated in semi-classical gravity, and relying on the existence of regular (complex) solutions of the equations of motion. We show by explicit computation that regular no-boundary solutions are modified, but not destroyed, upon inclusion of expected quantum gravity corrections that involve higher powers of the Riemann tensor as well as covariant derivatives thereof. We illustrate our results with examples drawn from string theory. Our findings provide a crucial self-consistency test of the no-boundary framework.

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arXiv2020

Lessons for quantum cosmology from anti-de Sitter black holes

Gravitational physics is arguably better understood in the presence of a negative cosmological constant than a positive one, yet there exist strong technical similarities between the two settings. These similarities can be exploited to enhance our understanding of the more speculative realm of quantum cosmology, building on robust results regarding anti-de Sitter black holes describing the thermodynamics of holographic quantum field theories. To this end, we study 4-dimensional gravitational path integrals in the presence of a negative cosmological constant, and with minisuperspace metrics. We put a special emphasis on boundary conditions and integration contours. The Hawking-Page transition is recovered and we find that below the minimum temperature required for the existence of black holes the corresponding saddle points become complex. When the asymptotic anti-de Sitter space is cut off at a finite distance, additional saddle points contribute to the partition function, albeit in a very suppressed manner. These findings have direct consequences for the no-boundary proposal in cosmology, because the anti-de Sitter calculation can be brought into one-to-one correspondence with a path integral for de Sitter space with Neumann conditions imposed at the nucleation of the universe. Our results lend support to recent implementations of the no-boundary proposal focusing on momentum conditions at the "big bang".

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arXiv2019

A Safe Beginning for the Universe?

When general relativity is augmented by quadratic gravity terms, it becomes a renormalisable theory of gravity. This theory may admit a non-Gaussian fixed point as envisaged in the asymptotic safety program, rendering the theory trustworthy to energies up to the Planck scale and even beyond. We show that requiring physical solutions to have a finite action imposes a strong selection on big-bang-type universes. More precisely we find that, in the approach to zero volume, both anisotropies and inhomogeneities are suppressed while the scale factor is required to undergo accelerated expansion. This provides initial conditions which are favourable to the onset of an inflationary phase while also providing a suitable starting point for the second law of thermodynamics in the spirit of the Weyl curvature hypothesis.

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arXiv2019

Quantum Incompleteness of Inflation

Inflation is most often described using quantum field theory (QFT) on a fixed, curved spacetime background. Such a description is valid only if the spatial volume of the region considered is so large that its size and shape moduli behave classically. However, if we trace an inflating universe back to early times, the volume of any comoving region of interest -- for example the present Hubble volume -- becomes exponentially small. Hence, quantum fluctuations in the trajectory of the background cannot be neglected at early times. In this paper, we develop a path integral description of a flat, inflating patch (approximated as de Sitter spacetime), treating both the background scale factor and the gravitational wave perturbations quantum mechanically. We find this description fails at small values of the initial scale factor, because \emph{two} background saddle point solutions contribute to the path integral. This leads to a breakdown of QFT in curved spacetime, causing the fluctuations to be unstable and out of control. We show the problem may be alleviated by a careful choice of quantum initial conditions, for the background and the fluctuations, provided that the volume of the initial, inflating patch is larger than $\gg H^{-1}$ in Planck units with $H$ the Hubble constant at the start of inflation. The price of the remedy is high: not only the inflating background, but also the stable, Bunch-Davies fluctuations must be input by hand. Our discussion emphasizes that, even if the inflationary scale is far below the Planck mass, new physics is required to explain the initial quantum state of the universe.

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arXiv2019

Homogeneous Transitions during Inflation: a Description in Quantum Cosmology

The usual description of inflationary fluctuations uses the framework of quantum field theory (QFT) in curved spacetime, in which quantum fluctuations are superimposed on a classical background spacetime. Even for large fluctuations, such as those envisioned during a regime of eternal inflation, this framework is frequently used. In the present work we go one step beyond this description by quantising both the scalar field and the scale factor of the universe. Employing the Lorentzian path integral formulation of semi-classical gravity we restrict to a simplified minisuperspace setting by considering homogeneous transitions. This approach allows us to determine the dominant geometry and inflaton evolution contributing to such amplitudes. We find that for precisely specified initial scale factor and inflaton values (and uncertain momenta), two distinct saddle point geometries contribute to the amplitude, leading to interference effects. However, when the momenta of both scale factor and inflaton are specified with sufficient certainty, only a single saddle point is relevant and QFT in curved spacetime is applicable. In particular we find that for inflaton transitions up the potential, meaningful results are only obtained when the initial uncertainty in the inflaton value is large enough, allowing the dominant evolution to be a complexified slow-roll solution \emph{down} from a comparatively unlikely position higher up in the potential.

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arXiv2019

The No-Boundary Proposal as a Path Integral with Robin Boundary Conditions

Realising the no-boundary proposal of Hartle and Hawking as a consistent gravitational path integral has been a long-standing puzzle. In particular, it was demonstrated by Feldbrugge et al. that the sum over all universes starting from zero size results in an unstable saddle point geometry. Here we show that in the context of gravity with a positive cosmological constant, path integrals with a specific family of Robin boundary conditions overcome this problem. These path integrals are manifestly convergent and are approximated by stable Hartle-Hawking saddle point geometries. The price to pay is that the off-shell geometries do not start at zero size. The Robin boundary conditions may be interpreted as an initial state with Euclidean momentum, with the quantum uncertainty shared between initial size and momentum.

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arXiv2019

Kerr-NUT-de Sitter as an Inhomogeneous Non-Singular Bouncing Cosmology

We present exact non-singular bounce solutions of general relativity in the presence of a positive cosmological constant and an electromagnetic field, without any exotic matter. The solutions are distinguished by being spatially inhomogeneous in one direction, while they can also contain non-trivial electromagnetic field lines. The inhomogeneity may be substantial, for instance, there can be one bounce in one region of the universe and two bounces elsewhere. Since the bounces are followed by a phase of accelerated expansion, the metrics described here also permit the study of (geodesically complete) models of inflation with inhomogeneous initial conditions. Our solutions admit two Killing vectors and may be re-interpreted as the pathology-free interior regions of Kerr-de Sitter black holes with non-trivial NUT charge. Remarkably enough, within this cosmological context, the NUT parameter does not introduce any string singularity nor closed timelike curves but renders the geometry everywhere regular, eliminating the big bang singularity by means of a bounce.

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arXiv2019

Non-Singular Bounces Catalysed by Dark Energy

We investigate classically non-singular bounces caused by dark energy. In the presence of positive spatial curvature, vacuum energy, either in the form of a cosmological constant or a scalar field potential, allows for an open set of initial conditions leading to non-singular bounces, without any violation of the null energy condition. We study anisotropic Bianchi IX cosmologies, and demonstrate that they can even have multiple bounces, accompanied by intricate evolutions of the anisotropies that provide a non-singular analogue of mixmaster crunches. The relation of these solutions to more complete cosmological models, as well as to the recently proposed swampland criteria, are briefly discussed.

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arXiv2018

Inconsistencies of the New No-Boundary Proposal

In previous works, we have demonstrated that the path integral for {\it real, Lorentzian} four-geometries in Einstein gravity yields sensible results in well-understood physical situations, but leads to uncontrolled fluctuations when the "no boundary" condition proposed by Hartle and Hawking is imposed. In order to circumvent our result, new definitions for the gravitational path integral have been sought, involving specific choices for a class of {\it complex} four-geometries to be included. In their latest proposal, Diaz Dorronsoro {\it et al.}~\cite{DiazDorronsoro:2018wro} advocate integrating the lapse over a complex circular contour enclosing the origin. In this note we show that, like their earlier proposal, this leads to mathematical and physical inconsistencies and thus cannot be regarded as a basis for quantum cosmology. We also comment on Vilenkin and Yamada's recent modification of the "tunneling" proposal, made in order to avoid the same problems. We show that it leads to the breakdown of perturbation theory in a strong coupling regime.

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arXiv2018

Small-Field and Scale-Free: Inflation and Ekpyrosis at their Extremes

There is increasing evidence from string theory that effective field theories are only reliable over approximately sub-Planckian field excursions. The two most promising effective models for early universe cosmology, inflation and ekpyrosis, are mechanisms that, in order to address cosmological puzzles, must operate over vast expansion/energy ranges. This suggests that it might be appropriate to describe them using scaling laws. Here we combine these two ideas and demonstrate that they drive inflation and ekpyrosis to their extremes: inflation must start at ultra-slow-roll, and ekpyrosis at ultra-fast-roll. At face value, the implied spectra are overly tilted to the red, although in both cases minor departures from pure scale freedom bring the spectral indices within current observational bounds. These models predict a significant spectral running at a level detectable in the near future ($α_s \approx -10^{-3}$). Ekpyrotic models with minimal coupling are nevertheless ruled out, as they lead to levels of non-Gaussianity that are at least an order of magnitude too large. No such restrictions apply to models with a kinetic coupling between the two ekpyrotic scalar fields, and these remain the most promising ekpyrotic models. An additional swampland criterion that was recently proposed for the slope of the scalar field potential would however rule out all ultra-slow-roll models of inflation. Finally, we speculate on the existence of corresponding restrictions on the slope at negative potential values, which might lead to similarly severe constraints on ekpyrotic models.

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arXiv2018

Unstable no-boundary fluctuations from sums over regular metrics

It was recently shown by Feldbrugge et al. that the no-boundary proposal, defined via a Lorentzian path integral and in minisuperspace, leads to unstable fluctuations, in disagreement with early universe observations. In these calculations many off-shell geometries summed over in the path integral in fact contain singularities, and the question arose whether the instability might ultimately be caused by these off-shell singularities. We address this question here by considering a sum over purely regular geometries, by extending a calculation pioneered by Halliwell and Louko. We confirm that the fluctuations are unstable, even in this restricted context which, arguably, is closer in spirit to the original proposal of Hartle and Hawking. Elucidating the reasons for the instability of the no-boundary proposal will hopefully show how to overcome these difficulties, or pave the way to new theories of initial conditions for the universe.

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arXiv2017

No Rescue for the No Boundary Proposal

In recent work, we introduced Picard-Lefschetz theory as a tool for defining the Lorentzian path integral for quantum gravity in a systematic semiclassical expansion. This formulation avoids several pitfalls occurring in the Euclidean approach. Our method provides, in particular, a more precise formulation of the Hartle-Hawking no boundary proposal, as a sum over real Lorentzian four-geometries interpolating between an initial three-geometry of zero size, {\it i.e}, a point, and a final three-geometry. With this definition, we calculated the no boundary amplitude for a closed universe with a cosmological constant, assuming cosmological symmetry for the background and including linear perturbations. We found the opposite semiclassical exponent to that obtained by Hartle and Hawking for the creation of a de Sitter spacetime "from nothing". Furthermore, we found the linearized perturbations to be governed by an {\it inverse} Gaussian distribution, meaning they are unsuppressed and out of control. Recently, Diaz Dorronsoro {\it et al.} followed our methods but attempted to rescue the no boundary proposal by integrating the lapse over a different, intrinsically complex contour. Here, we show that, in addition to the desired Hartle-Hawking saddle point contribution, their contour yields extra, non-perturbative corrections which again render the perturbations unsuppressed. We prove there is {\it no} choice of complex contour for the lapse which avoids this problem. We extend our discussion to include backreaction in the leading semiclassical approximation, fully nonlinearly for the lowest tensor harmonic and to second order for all higher modes. Implications for quantum de Sitter spacetime and for cosmic inflation are briefly discussed.

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arXiv2017

Spinor driven cosmic bounces and their cosmological perturbations

When coupling fermions to gravity, torsion is naturally induced. We consider the possibility that fermion bilinears can act as a source for torsion, altering the dynamics of the early universe such that the big bang gets replaced with a classical non-singular bounce. We extend previous studies in several ways: we allow more general fermion couplings, consider both commuting and anti-commuting spinors, and demonstrate that with an appropriate choice of potential one can easily obtain essentially arbitrary equations of state, including violations of the null energy condition, as required for a bounce. As an example, we construct a model of ekpyrotic contraction followed by a non-singular bounce into an expanding phase. We analyze cosmological fluctuations in these models, and show that the perturbations can be rewritten in real fluid form. We find indications that spinor bounces are stable, and exhibit several solutions for the perturbations. Interestingly, spinor models do not admit a scalar-vector-tensor decomposition, and consequently some types of scalar fluctuations can act as a source for gravitational waves already at linear order. We also find that the first order dynamics are directionally dependent, an effect which might lead to distinguished observational signatures.

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arXiv2017

No smooth beginning for spacetime

We identify a fundamental obstruction to any theory of the beginning of the universe, formulated as a semiclassical path integral. Hartle and Hawking's no boundary proposal and Vilenkin's tunneling proposal are examples of such theories. Each may be formulated as the quantum amplitude for obtaining a final 3-geometry by integrating over 4-geometries. We introduce a new mathematical tool - Picard-Lefschetz theory - for defining the semiclassical path integral for gravity. The Lorentzian path integral for quantum cosmology with a positive cosmological constant is meaningful in this approach, but the Euclidean version is not. Framed in this way, the resulting framework and predictions are unique. Unfortunately, the outcome is that primordial tensor (gravitational wave) fluctuations are unsuppressed. We prove a general theorem to this effect, in a wide class of theories.

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