Escher in the Sky

The cosmological models called $\alpha$-attractors provide an excellent fit to the latest observational data. Their predictions $n_{s} = 1-2/N$ and $r = 12\alpha/N^{2}$ are very robust with respect to the modifications of the inflaton potential. An intriguing interpretation of $\alpha$-attractors is based on a geometric moduli space with a boundary: a Poincare disk model of a hyperbolic geometry with the radius $\sqrt{3\alpha}$, beautifully represented by the Escher's picture Circle Limit IV. In such models, the amplitude of the gravitational waves is proportional to the square of the radius of the Poincare disk.Comment: 11 pages, 12 figures, Introductory part is extended, references adde

Paving the way for transitions --- a case for Weyl geometry

This paper presents three aspects by which the Weyl geometric generalization of Riemannian geometry, and of Einstein gravity, sheds light on actual questions of physics and its philosophical reflection. After introducing the theory's principles, it explains how Weyl geometric gravity relates to Jordan-Brans-Dicke theory. We then discuss the link between gravity and the electroweak sector of elementary particle physics, as it looks from the Weyl geometric perspective. Weyl's hypothesis of a preferred scale gauge, setting Weyl scalar curvature to a constant, gets new support from the interplay of the gravitational scalar field and the electroweak one (the Higgs field). This has surprising consequences for cosmological models. In particular it leads to a static (Weyl geometric) spacetime with "inbuilt" cosmological redshift. This may be used for putting central features of the present cosmological model into a wider perspective.Comment: 54 pp, 2 figs. To appear in D. Lehmkuhl (ed.) "Towards a Theory of Spacetime Theories", Einstein Studies, Basel: Birkhaeuser), revised version June 201

Integrability of anisotropic and homogeneous Universes in scalar-tensor theory of gravitation

In this paper, we develop a method based on the analysis of the Kovalewski exponents to study the integrability of anisotropic and homogeneous Universes. The formalism is developed in scalar-tensor gravity, the general relativistic case appearing as a special case of this larger framework. Then, depending on the rationality of the Kovalewski exponents, the different models, both in the vacuum and in presence of a barotropic matter fluid, are classified, and their integrability is discussed.Comment: 16 pages, no figure, accepted in CQ

Vacuum decay in an interacting multiverse

We examine a new multiverse scenario in which the component universes interact. We focus our attention to the process of "true" vacuum nucleation in the false vacuum within one single element of the multiverse. It is shown that the interactions lead to a collective behaviour that might lead, under specific conditions, to a pre-inflationary phase and ensued distinguishable imprints in the comic microwave background radiation.Comment: 9 pages, 5 figure

Are quantization rules for horizon areas universal?

Doubts have been expressed on the universality of holographic/string-inspired quantization rules for the horizon areas of stationary black holes or the products of their radii, already in simple 4-dimensional general relativity. Realistic black holes are not stationary but time-dependent. Using two examples of 4D general-relativistic spacetimes containing dynamical black holes for at least part of the time, it is shown that the quantization rules (even counting virtual horizons) cannot hold, except possibly at isolated instants of time, and do not seem to be universal.Comment: One example and one figure added, two figures improved, bibliography expanded and updated. Matches the version accepted for publication in Phys. Rev.