[en] Because the inflationary mechanism is extremely sensitive to UV-physics, the construction of theoretically robust models of inflation provides a unique window on Planck scale physics. We review efforts to use an axion with a shift symmetry to ensure a prolonged slow-roll background evolution. The symmetry dictates which operators are allowed, and these in turn determine the observational predictions of this class of models, which include observable gravitational waves (potentially chiral), oscillations in all primordial correlators, specific deviations from scale invariance and Gaussianity and primordial black holes. We discuss the constraints on this class of models in light of the recent Planck results and comment on future perspectives. The shift symmetry is very useful in models of large-field inflation, which typically have monomial potentials, but it cannot explain why two or more terms in the potential are fine-tuned against each other, as needed for typical models of small-field inflation. Therefore some additional symmetries or fine tuning will be needed if forthcoming experiments will constrain the tensor-to-scalar ratio to be r ≲ 0.01. (paper)

[en] We consider the quantization of linearized fluctuations of the metric and matter fields about a Lifshitz background, exploring the possibility of alternative boundary conditions, allowing the slow fall-off modes to fluctuate. We find that for z > 2, slow fall-off modes for some of the linearized fluctuations are normalizable, which opens up the possibility of considering alternative boundary conditions. Analysing stability, we find that alternative boundary conditions for the momentum density are allowed, but alternative boundary conditions for the energy density lead to an instability of the type we recently discovered in a similar analysis for scalar fields on a fixed Lifshitz background. Our investigation is in the context of the simple massive vector model, but we would expect the conclusions to be more general. (paper)

[en] We perform a phase-space analysis of the cosmological 3-fluid problem consisting of a barotropic fluid with an equation-of-state parameter γ − 1, a pressureless dark matter fluid, plus a scalar field ϕ (representing dark energy) coupled to an exponential potential V = V₀exp ( − κλϕ). Besides the potential–kinetic scaling solutions, which are not the unique late-time attractors whenever they exist for λ² ⩾ 3γ, we derive new attractors where both dark energy and dark matter coexist and the final density is shared in a way independent of the value of γ > 1. The case of a pressureless barotropic fluid (γ = 1) has a one-parameter family of attractors where all components coexist. New one-parameter families of matter–dark matter saddle points and kinetic–matter repellers exist. We investigate the stability of the ten critical points by linearization and/or Lyapunov's theorems and a variant of the theorems formulated in this paper. A solution with two transient periods of acceleration and two transient periods of deceleration is derived. (paper)

[en] In this paper we explore observational bounds on flat and non-flat cosmological models in type II Randall–Sundrum branes. In a first analysis, we consider current measurements of the expansion rate H(z) (with two priors on the local Hubble parameter) and 288 type Ia supernovae from the Sloan digital sky survey (within the framework of the mlcs2k2 light-curve fitting method). We find that the joint analysis involving these data is an interesting tool to impose limits on the brane tension density parameter (Ω_λ) and that the spatial curvature has a negligible influence on Ω_λ estimates. In order to obtain stronger bounds for the contribution of Ω_λ, we also add in our analysis the baryon oscillation (BAO) peak and cosmic microwave background (CMB) radiation observations by using the so-called CMB/BAO ratio. From this analysis we find that the Ω_λ contribution is less than 4.10⁻⁵ (1σ). (paper)

[en] Motivated by the quasi-local mass problem in general relativity, we apply the asymptotically flat extensions, constructed by Shi and Tam in the proof of the positivity of the Brown–York mass, to study a fill-in problem of realizing geometric data on a 2-sphere as the boundary of a compact 3-manifold of non-negative scalar curvature. We characterize the relationship between two borderline cases: one in which the Shi–Tam extension has zero total mass, and another in which fill-ins of non-negative scalar curvature fail to exist. Additionally, we prove a type of positive mass theorem in the latter case. (paper)

[en] We study the Cauchy problem in a special case of nonlinear massive gravity. Despite being ghost free, it has recently been argued that the theory is inherently problematic due to the existence of superluminal shock waves. Furthermore, it is claimed that an acausal characteristic can arise for any choice of background. In order to further understand the causal structure of the theory, we carefully perform a detailed analysis of the characteristic equations and show that the theory does admit a well-posed Cauchy problem, i.e., there exists hypersurfaces that are not a characteristic hypersurface. Puzzles remain regarding the existence of a superluminal propagating mode in both the minimal ghost-free theory that we analyzed, as well as in the full nonlinear massive gravity. That is, our result should not be taken as any indication of the healthiness of the theory. We also give a detailed review of Cauchy–Kovalevskaya theorem and its application in the appendix, which should be useful for investigating causal structures of other theories of gravity. (paper)

[en] A shared property of several of the known exact solutions to the equations of force-free electrodynamics is that their charge-current four-vector is null. We examine the general properties of null-current solutions and then focus on the principal congruences of the Kerr black hole spacetime. We obtain a large class of exact solutions, which are in general time-dependent and non-axisymmetric. These solutions include waves that, surprisingly, propagate without scattering on the curvature of the black hole’s background. They may be understood as generalizations to Robinson’s solutions to vacuum electrodynamics associated with a shear-free congruence of null geodesics. When stationary and axisymmetric, our solutions reduce to those of Menon and Dermer, the only previously known solutions in Kerr. In Kerr, all of our solutions have null electromagnetic fields ( E-vector · B-vector = 0 and E² = B²). However, in Schwarzschild or flat spacetime there is freedom to add a magnetic monopole field, making the solutions magnetically dominated (B² > E²). This freedom may be used to reproduce the various flat-spacetime and Schwarzschild-spacetime (split) monopole solutions available in the literature (due to Michel and later authors), and to obtain a large class of time-dependent, non-axisymmetric generalizations. These generalizations may be used to model the magnetosphere of a conducting star that rotates with arbitrary prescribed time-dependent rotation axis and speed. We thus significantly enlarge the class of known exact solutions, while organizing and unifying previously discovered solutions in terms of their null structure. (paper)

[en] In this paper we elucidate the rigid limit of N = 2 supergravity coupled to vector and hypermultiplets. In particular we show how the respective scalar field spaces reduce to their global counterparts. In the hypermultiplet sector we focus on the relation between the local and rigid c-map. (paper)

[en] We obtain the first black hole solution to Type-IIA String Theory compactified on an arbitrary self-mirror Calabi–Yau manifold in the presence of non-perturbative quantum corrections. Remarkably enough, the solution involves multivalued functions, which could lead to a violation of the No-Hair conjecture. We discuss how String Theory forbids such scenario. However, the possibility still remains open in the context of four-dimensional ungauged Supergravity. (paper)

[en] A defining feature of holographic dualities is that, along with the bulk equations of motion, boundary correlators at any given time t determine those of observables deep in the bulk. We argue that this property emerges from the bulk gravitational Gauss law together with bulk quantum entanglement as embodied in the Reeh–Schlieder theorem. Stringy bulk degrees of freedom are not required and play little role even when they exist. As an example we study a toy model whose matter sector is a free scalar field. The energy density ρ sources what we call a pseudo-Newtonian potential Φ through Poisson’s equation on each constant time surface, but there is no back-reaction of Φ on the matter. We show the Hamiltonian to be essentially self-adjoint on the domain generated from the vacuum by acting with boundary observables localized in an arbitrarily small neighborhood of the chosen time t. Since the Gauss law represents the Hamiltonian as a boundary term, the model is holographic in the sense stated above. (paper)