Jackiw-Teitelboim (JT) gravity in two-dimensional de Sitter space is an intriguing model for cosmological “wave functions of the universe”. Its minisuperspace version already contains all physical information. The size of compact slices is parametrized by a scale factor $\textit{h}$ > 0. The dilaton $\textit{ϕ}$ is chosen to have positive values and interpreted as size of an additional compact slice in a higher-dimensional theory. At the boundaries $\textit{h}$ = 0, $\textit{ϕ}$ = 0, where the volume of the universe vanishes, the curvature is generically singular. According to a conjecture by DeWitt, solutions of the Wheeler-DeWitt (WDW) equation should vanish at singular loci. Recently, the behaviour of JT wave functions at large field values $\textit{h}$, $\textit{ϕ}$ has been obtained by means of a path integral over Schwarzian degrees of freedom of a boundary curve. We systematically analyze solutions of the WDW equation with Schwarzian asymptotic behaviour. We find real analytic solutions that vanish on the entire boundary, in agreement with DeWitt’s conjecture. Projection to expanding and contracting branches may lead to singularities, which can however be avoided by an appropriate superposition of solutions. Our analysis also illustrates the limitations of semiclassical wave functions.

Germany

Wilfried Buchmüller

Arthur Hebecker

Alexander Westphal

DeWitt wave functions for de Sitter JT gravity

Making cosmological predictions in a multiverse is a fundamental theoretical challenge. Assuming that (quasi-)de Sitter vacua are quantum mechanically described by a finite-dimensional Hilbert space, we develop a detailed framework for making explicit anthropic predictions. A key challenge which we attempt to overcome arises because, almost unavoidably, cosmologies that asymptote to Minkowski space exist. We then apply our framework to predicting the scale of inflation. We find that, even if eternal inflation is allowed, our predictions depend on creation rates of universes from nothing. These, in turn, are highly sensitive to the existence of end-of-the-world branes. The rates for the creation of universes from nothing are the dominant ingredient for ‘Swampy Landscapes’, which may have no metastable de Sitter vacua but only slow-roll solutions. In ‘Rocky Landscapes’, where long-lived de Sitter vacua are abundant, tunneling rates between such vacua represent a further key factor for deriving predictions.

Bjoern Friedrich

End-of-the-world branes and inflationary predictions for rocky and swampy landscapes

One of the leading ideas for the beginning of the Universe is the Hartle-Hawking ‘No-Boundary Proposal.’ Since the Cobordism Conjecture claims that any spacetime allows for a dynamical boundary, we suggest that one may equally well consider a ‘Boundary Proposal’. Specifically, the corresponding euclidean instanton is a sphere with two holes around north and south pole cut out. Analogously to the Hartle-Hawking proposal, the sphere is then cut in two at the equator and half of it is dropped. The equator is glued to an expanding Lorentzian de Sitter space, implementing a beginning of the Universe with a spacelike spherical boundary at its earliest moment. This process is in principle on equal footing with the one based on the no-boundary instanton. In fact, if the Linde-Vilenkin sign choice is used, this ‘Boundary’ creation process may even dominate. An intriguing implication arises if tensionless end-of-the-world branes, as familiar from type-IIA or M-theory, are available: Analogously to the Boundary Proposal, one may then be able to create a compact, flat torus universe from nothing, without any exponential suppression or enhancement factors.

The boundary proposal

We present a new model of string inflation driven by a blow-up Kähler modulus of type IIb compactifications with a potential generated by string loops. Slow-roll is naturally realized thanks to the fact that the blow-up mode is a leading-order flat direction lifted by string loops which are unavoidable and generate a plateau at large field values. We check that throughout the whole inflationary dynamics the effective field theory is under control. We perform a phenomenological analysis determining the exact number of efoldings by studying the post-inflationary evolution. We determine the values of the microscopic parameters which lead to agreement with CMB data, together with the prediction of a tensor-to-scalar ratio of order r ∼ 10 −5.

Sukṛti Bansal

Italy

Luca Brunelli

Michele Cicoli

Ruben Kuespert

Loop blow-up inflation

Kinetic mixing between gauge fields of different U(1) factors is a well-studied phenomenon in 4d EFT. In string compactifications with U(1)s from sequestered D-brane sectors, kinetic mixing becomes a key target for the UV prediction of a phenomenologically important EFT operator. Surprisingly, in many cases kinetic mixing is absent due to a non-trivial cancellation. In particular, D3-D3 kinetic mixing in type-IIB vanishes while D3-anti-D3 mixing does not. This follows both from exact CFT calculations on tori as well as from a leading-order 10d supergravity analysis, where the key cancellation is between the C 2 and B 2 contribution. We take the latter approach, which is the only one available in realistic Calabi-Yau settings, to a higher level of precision by including sub-leading terms of the brane action and allowing for non-vanishing C 0. The exact cancellation persists, which we argue to be the result of  $${\text{SL}}\left(2,{\mathbb{R}}\right)$$  self-duality. We note that a B 2 C 2 term on the D3-brane, which is often missing in the recent literature, is essential to obtain the correct zero result. Finally, allowing for  $${\text{SL}}\left(2,{\mathbb{R}}\right)$$ -breaking fluxes, kinetic mixing between D3-branes arises at a volume-suppressed level. We provide basic explicit formulae, both for kinetic as well as magnetic mixing, leaving the study of phenomenologically relevant, more complex situations for the future. We also note that describing our result in 4d supergravity appears to require higher-derivative terms — an issue which deserves further study.

Joerg Jaeckel

Small kinetic mixing in string theory

We study bubble of nothing decays and their reverse processes, the creation of vacua through ‘bubbles of something’, in models of the Universe based on string theory. From the four-dimensional perspective, the corresponding gravitational instantons contain an end-of-the-world (ETW) boundary or brane, realized by the internal manifold shrinking to zero size. The existence of such ETW branes is predicted by the Cobordism Conjecture. We develop the 4d EFT description of such boundaries at three levels: first, by generalizing the Witten bubble through an additional defect. Second, by replacing the compact S 1 with a Calabi-Yau orientifold and allowing it to shrink and disappear through a postulated defect. Third, we describe an ETW brane construction for type IIB Calabi-Yau orientifold compactifications with O3/O7 planes through an appropriate additional O5 orientifolding. Our 4d EFT formalism allows us to compute the decay/creation rates for bubbles of anything depending on two parameters: the size of the relevant defect and its tension a.k.a. the induced (generalized) deficit angle.

Johannes Walcher

Cobordism and bubbles of anything in the string landscape

There has recently been considerable interest in the question whether and under which conditions accelerated cosmological expansion can arise in the asymptotic regions of field space of a -dimensional EFT. We conjecture that such acceleration is impossible unless there exist metastable de Sitter vacua in more than dimensions. That is, we conjecture that ‘Asymptotic Acceleration Implies de Sitter’ (AA⇒DS). Phrased negatively, we argue that the -dimensional ‘No Asymptotic Acceleration’ conjecture (a.k.a. the ‘strong asymptotic dS conjecture’) follows from the de Sitter conjecture in more than dimensions. The key idea is that the relevant field-space asymptotics almost always correspond to decompactification and that the only positive energy contribution which decays sufficiently slowly in this regime is the vacuum energy of a higher-dimensional metastable vacuum. This result is in agreement with recent Swampland bounds on the potential in the asymptotics in field space from e.g. the species bound, but is significantly more constraining. We further note that for our asymptotic decompactification limits based on higher-dimensional de Sitter, the Kaluza-Klein scale always falls below the Hubble scale asymptotically. In fact, this occurs whenever $$ \left|{V}^{\prime}\right|/V\le 2\sqrt{\left(d+k-2\right)/k\left(d-2\right)} $$ asymptotically, with the number of decompactifying internal directions. This is steeper than what is needed for accelerated expansion.

Simon Schreyer

Victoria Venken

No asymptotic acceleration without higher-dimensional de Sitter vacua

According to the ‘Cosmological Central Dogma’, de Sitter space can be viewed as a quantum mechanical system with a finite number of degrees of freedom, set by the horizon area. We use this assumption together with the Wheeler-DeWitt (WDW) equation to approach the measure problem of eternal inflation. Thus, our goal is to find a time-independent wave function of the universe on a total Hilbert space defined as the direct sum of a variety of subspaces: A finite-dimensional subspace for each de Sitter vacuum and an infinite-dimensional subspace for each terminal Minkowski or AdS vacuum. We argue that, to be consistent with semiclassical intuition, such a solution requires the presence of sources. These are implemented as an inhomogenous term in the WDW equation, induced by the Hartle-Hawking no-boundary or the Linde/Vilenkin tunneling proposal. Taken together, these steps unambiguously lead to what we would like to think of as a ‘Local WDW measure,’ where ‘local’ refers to the fact that the dS part of the resulting wave function describes a superposition of static patches. The global 3-sphere spatial section of the entire multiverse makes no appearance.

Manfred Salmhofer

Jonah Cedric Strauß

A local Wheeler-DeWitt measure for the string landscape

We consider ′ curvature corrections to the action of an NS5-brane which plays the key role in the metastability analysis of warped anti-D3-brane uplifts by Kachru, Pearson and Verlinde (KPV). Such corrections can dramatically alter the KPV analysis. We find that for the ′ -corrections to be sufficiently small to recover essentially the leading-order KPV potential one needs a surprisingly large radius, corresponding to > 20. In the context of the Large Volume Scenario (LVS) this implies a D3-tadpole of at least (10 –10 ). However, large ′ -corrections do not necessarily spoil the uplift in KPV. Rather, as the curvature corrections lower the tension of the brane, a novel uplifting mechanism suggests itself where the smallness of the uplift is achieved by a tuning of curvature corrections. A key underlying assumption is the existence of a dense discretuum of . This new mechanism does not require a deep warped throat, thereby sidestepping the main difficulty in uplifting KKLT and LVS. However, all of the above has to be treated as a preliminary exploration of possibilities since, at the moment, not all relevant corrections at the order ′ are known.

Curvature corrections to KPV: do we need deep throats?

It is widely believed that string theory easily allows for a QCD axion in the cosmologically favored mass range. The required small decay constant, f  a  ≪ M  P , can be implemented by using a large compactification volume. This points to the Large Volume Scenario which in turn makes certain cosmological predictions: first, the closed string axion behaves similarly to a field-theoretic axion in the pre-inflationary scenario, i.e. the initial value can be tuned but one is constrained by isocurvature fluctuations. In addition, the volume represents a long-lived modulus that may lead to an early matter-dominated phase. Finally, the decay of the volume modulus to its own axion tends to overproduce dark radiation. In this paper we aim to carefully analyze the cosmology by studying models that not only allow for a QCD axion but also include inflation. Quite generally, limits on isocurvature fluctuations restrict us to relatively low-scale inflation, which in the present stringy context points to Kähler moduli inflation. As a novel feature we find that the lightest (volume) modulus couples strongly to the Higgs. It hence quickly decays to the SM, thus resolving the original dark radiation problem. This decay is much faster than that of the inflaton, implying that reheating is determined by the inflaton decay. The inflaton could potentially reintroduce a dark radiation problem since it decays to lighter moduli and their axions with equal rates. However, due its mixing with the QCD-saxion, the inflaton has also a direct decay rate to the SM, enhanced by the number of SM gauge bosons. This results in an amount of dark radiation that is consistent with present limits but potentially detectable in future measurements.