General Relativity & Quantum Cosmology

I briefly introduce the recently introduced idea of relativity of locality, which is a consequence of a non-flat geometry of momentum space. Momentum space can acquire nontrivial geometrical properties due to quantum gravity effects. I study the relation of this framework with noncommutative geometry, and the Quantum Group approach to noncommutative spaces. In particular I'm interested in kappa-Poincaré, which is a Quantum Group that, as shown by Freidel and Livine, in the 1+1D case emerges as the symmetry of effective field theory coupled with quantum gravity, once that the gravitational degrees of freedom are integrated out. I'm interested in particular in the Lorentz covariance of this model which is present, but is realized in a nontrivial way. If I still have time, I'll then speak about an under-course general study of the Lorentz covariance of Relative Locality models.

The development of virial mass estimates for the central black hole using one quasar spectrum has allowed a dramatic improvement in our understanding of supermassive black hole evolution. I will describe several new puzzles arising from the combination of virial masses with luminosity and redshift measurements, many of which are inconsistent with our current understanding of quasar evolution. I will also describe a new class of quasars that does not appear to fit easily into current models for quasar accretion.

This talk will deal with a new connection formulation for higher-dimensional (Super)gravity theories and its applications. We will start by reviewing the basic ideas of loop quantum gravity. Next, the derivation of the new connection formulation will be discussed and it will be shown that the quantization methods developed in the context of loop quantum gravity apply. We comment on applications of the framework, focusing on making contact with String theory.

In inflationary theories, single field models are typically considered subject to slow-roll conditions. In this talk I will present current observational constraints on deviations from slow-roll, e.g. bounds coming from strong coupling considerations, scale-dependent non-Gaussianities and the tensor-to-scalar ratio. These constraints still allow significant violations of slow-roll conditions. Focusing on non-Gaussian signals, I will discuss a variety of intriguing observable signatures that can be found for fast-rolling single fields.

The parity invariance of spinfoam gravity is an open question. Naively, parity breaking should reside in the sign of the Immirzi parameter. I show that the new Lorentzian vertex formula is in fact independent of this sign, suggesting that the dynamics is parity-invariant. The situation with boundary states and operators is more complicated. I discuss parity-related pieces of the transition amplitude and graviton propagator in the large-spin 4-simplex limit. Numerical results indicate patterns similar to those in the Euclidean case. In particular, parity-related components of the graviton propagator differ by a phase. I discuss possible resolutions of this issue.

We provide a microscopic understanding of the nucleation of topological quantum liquids that arise due to interactions between non-Abelian anyons. With the pairwise anyon interactions typically showing RKKY-type oscillations in sign, but decaying exponentially with distance, we show that the character of the nucleated phase is fully determined by anyon interactions beyond nearest neighbor exchange. We investigate this issue in the context of Kitaev's honeycomb lattice model. In the presence of vortex lattices, depending on microscopic parameters such as the vortex lattice spacing, we observe the nucleation of several distinct Abelian topological phases, that differ in their band structure and Chern number description. By employing an effective model of Majorana fermions, we show that these phases can be fully predicted from the vortex-vortex interactions. Corresponding microscopic results should hold for vortices forming an Abrikosov lattice in a p-wave superconductor or quasiholes forming a Wigner crystal in non-Abelian quantum Hall states.

Bizon and Rostworowski have recently suggested that anti-de Sitter spacetime might be nonlinearly unstable to transfering energy to smaller and smaller scales and eventually forming a small black hole. We consider pure gravity with a negative cosmological constant and find strong support for this idea. While one can start with a single linearized mode and add higher order corrections to construct a nonlinear geon, this is not possible starting with a linear combination of two or more modes. One is forced to add higher frequency modes with growing amplitude. The implications of this turbulent instability for the dual field theory are discussed.

This talk focuses on an application of a WKB technique that is a generalization of the Born-Oppenheimer approximation to the Schwinger model of angular momentum. This work makes it possible to express the asymptotic limits of higher 3nj symbols in terms of the asymptotic limits of lower 3nj symbols, when only a subset of quantum numbers are taken to be large. After an introduction of the the technique, we show that the 15j symbol has different asymptotic limits in terms of a combination of several Ponzano Regge actions when different subsets of quantum numbers are taken large.

Constant mean curvature (uniform K) hypersurfaces extend to future null infinity in asymptotically flat spacetimes. With conformal compactification, the entire hypersurface can be covered by a finite spatial grid, eliminating any need an "outgoing wave" boundary condition or for extrapolation to find gravitational wave amplitudes. I will discuss the asymptotic behavior near future null infinity, how this can be simplified by suitable gauge conditions, and how this determines the physical Bondi energy and momentum of the system. Numerical results for how Bowen-York parameters in the conformally flat initial value problem are related to the physical energy and momentum in systems with single and binary black holes will be presented.

Most predictions for binary compact object formation are normalized to the present-day Milky Way population. In this talk, I suggest the merger rate of black hole binaries could be exceptionally sensitive to the ill-constrained fraction of low-metallicity star formation that ever occurred on our past light cone. I discuss whether and how observations might distinguish binary evolution uncertainties from this strong trend, both in the near future with well-identified electromagnetic counterparts and in the more distant future via third-generation gravitational wave detectors.

Supernovae observations strongly support the presence of a cosmological constant, but its value, which we will call apparent, is normally determined assuming that the Universe can be accurately described by a homogeneous model. Even in the presence of a cosmological constant we cannot exclude nevertheless the presence of a small local inhomogeneity which could affect the apparent value of the cosmological constant. Neglecting the presence of the inhomogeneity can in fact introduce a systematic misinterpretation of cosmological data, leading to the distinction between an apparent and true value of the cosmological constant. We establish the theoretical framework to calculate the corrections to the apparent value of the cosmological constant by modeling the local inhomogeneity with a $\Lambda LTB$ solution. Our assumption to be at the center of a spherically symmetric inhomogeneous matter distribution correspond to effectively calculate the monopole contribution of the non linear inhomogeneities surrounding us, which we expect to be the dominant one, because of other observations supporting a high level of isotropy of the Universe around us. By performing a local Taylor expansion we analyze the number of independent degrees of freedom which determine the local shape of the inhomogeneity, and consider the issue of central smoothness, showing how the same correction can correspond to different inhomogeneity profiles. Contrary to previous attempts to fit data using large void models our approach is quite general. The correction to the apparent value of the cosmological constant is in fact present for local inhomogeneity of any size, and should always be taken appropriately into account both theoretically and observationally.