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.

Germany

Bjoern Friedrich

Arthur Hebecker

Alexander Westphal

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 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

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.