General Relativity & Quantum Cosmology

In the geometric models of matter, proposed in a joint paper with Michael Atiyah and Nick Manton, static particles like the electron or proton are modelled by Riemannian 4-manifolds. In this talk I will explain how the spin degrees of freedom appear in the geometric framework. I will also discuss a proposal for time evolution in one particular model, namely the Taub-NUT model of the electron.

In the geometric models of matter, proposed in a joint paper with Michael Atiyah and Nick Manton, static particles like the electron or proton are modelled by Riemannian 4-manifolds. In this talk I will explain how the spin degrees of freedom appear in the geometric framework. I will also discuss a proposal for time evolution in one particular model, namely the Taub-NUT model of the electron.

 

Inspired by recent progress into recasting dissipative fluid dynamics within an effective action formalism,

I will show how to embed this problem in holography, where such effective actions can be computed explicitly for the class of relativistic conformal fluids. In particular I will identify the geometric counterpart of certain Goldstone bosons, the light degrees of freedom responsible for the low energy excitations in hydrodynamics. Moreover I will show how the underlying UV Schwinger-Keldysh structure arises at the level of the effective action.

The fact that the Einstein-Hilbert action, by itself, does not lead to a well-posed variational principle has become textbook knowledge. It can be made well-posed by the addition of suitable boundary terms. There are many boundary terms available in the literature, of which the most famous and most widely used is the Gibbons-Hawking-York (GHY) boundary term. The GHY term is ostensibly defined only for a non-null boundary. There have been very few efforts in the literature to extend its definition to null boundaries. The speaker will present his group's work towards finding a boundary term to render the Einstein-Hilbert action well-posed in the presence of null boundaries. He shall discuss a proposed boundary term, associated boundary conditions, outstanding issues and possible applications.

I will present recent result on constructing effective quantum gravity theory as a locally covariant QFT. The approach I advocate uses the BV formalism for dealing with the gauge freedom and Epstein-Glaser renormalization to control the UV divergences. I will show how gauge invariant observables that satisfy a weak notion of locality can be constructed in this framework and I will sketch the argument for perturbative background independence. Recently these ideas were applied to models relevant in cosmology.

In this talk I discuss the effects of nonlinear backreaction of small scale density inhomogeneities in general relativistic cosmology. It has been proposed that in an inhomogeneous universe, nonlinear terms in the Einstein equation could, if properly averaged and taken into account, affect the large scale Friedmannian evolution of the universe. In particular, it was hoped that these terms might mimic a cosmological constant and eliminate the need for dark energy. After reviewing some of these approaches, and some of their flaws, I will describe a perturbative framework (developed with R. Wald) designed to properly take into account these effects. In our framework, we assume that the spacetime metric is "close"---within 1 part in 10^4, except near strong field objects---to a background metric of FLRW symmetry, but we do not assume that the background metric satisfies the Friedmann equation. We also do not require that spacetime derivatives of the metric be close to derivatives of the background metric. This allows for significant deviations in geodesics, and very large curvature inhomogeneities. A priori, this framework also allows for significant backreaction, which would take the form of new effective matter sources in the Friedmann equation. Nevertheless, we prove that if the matter stress-energy tensor satisfies the weak energy condition, then large matter inhomogeneities on small scales cannot produce significant backreaction effects on large scales, and in particular cannot account for dark energy. As I will also review here, with a suitable ‘dictionary,’ Newtonian cosmologies provide excellent approximations to cosmological solutions to Einsteinʼs equation (with dust and a cosmological constant) on all scales. Our results thereby provide strong justification for the mathematical consistency and validity of the LCDM model within the context of general relativistic cosmology. While our rigorous framework makes use of 1-parameter families and weak limits, in this talk I will provide a simple heuristic discussion that places emphasis on the manner in which "averaging" is done, and the fact that one is solving the Einstein equation.

The precise determination of the entanglement of an interacting quantum many-body systems is now appreciated as an indispensable tool to identify the fundamental character of the ground state of such systems. This is particularly true for unconventional ground states harbouring non-local topological order or so-called quantum spin liquids that evade a standard description in terms of correlation functions. With the entanglement entropy emerging as one of the central measures of entanglement, recent progress has focused on a precise characterization of its scaling behaviour, in particular in the determination of (subleading) corrections to the prevalent boundary-law. 

In the past years, much progress has been made for certain spin, bosonic, and even fermionic quantum many-body systems. However, a large class of interacting models is thought to be exempt from numerical studies due to the fermion sign problem. At its heart, it occurs when the statistical weights in the simulation are positive and negative resulting in an exponential scaling of the algorithm instead of a polynomial one. In this work, we study the connection of the sign problem and the entanglement entropy using Determinantal Quantum Monte Carlo, the method of choice for unbiased, large-scale simulations of fermionic systems. We show that there is a strong correlation between the behavior of the entanglement entropy and the sign problem and that the particular structure of the ‘observable’ entanglement entropy to some extent allows to handle the sign problem much better than for usual correlation functions.

The Advanced LIGO observatories have successfully completed their first science run. Data were collected from September 2015 to January 2016, with a sensitivity a few times better than initial instruments in the hundreds of Hertz band. In this talk I will describe the searches for gravitational-wave transients performed during the first few weeks of the science run. Furthermore, I will describe the methods devised to characterize transient gravitational-wave sources and their applications in the advanced gravitational-wave detector era.

Generation of accurate mock observations tailored specifically to upcoming surveys such as Advanced ACT, CHIME, and LSST is a key technical challenge in cosmology. Traditional approaches involving N-body simulation are fraught with difficulties due to increasingly large survey volumes and depths. Typically, statistical ensembles can only be realized for a few carefully-chosen parameters, limiting exploration to a significantly restricted cosmological model space. We have developed a new massively parallel algorithm to generate accurate halo masses and positions in a fraction (~1e-3 to 1e-2) of the time taken by N-body simulations. I will present a suite of simulated full sky cluster Sunyaev-Zel’dovich maps that have been produced with this approach, and describe the types of virtual large scale structure observations that are now within reach in the coming years.

One possibility for studying reheating is to link the duration and final temperature after reheating, and its equation of state, to inflationary observables. By restricting the equation of state to lie within a broad physically allowed range, one can bracket an allowed range of $n_s$ and $r$ for models of inflation. The results are similar to, but do a little better, than requiring the length of inflation lie between 50 and 60 efolds. The added constraints can help break degeneracies between inflation models that otherwise overlap in their predictions.

The collection of all Dirac operators for a given fermion space defines its space of geometries. 
Formally integrating over this space of geometries can be used to define a path integral and a thus a theory of quantum gravity. 
In general this expression is complicated, however for fuzzy spaces a simple expression for the general form of the Dirac operator exists. This simple expression allows us to explore the space of geometries using Markov Chain Monte Carlo methods and thus examine the path integral in a manner similar to that used in CDT. 
In doing this we find a phase transition and indications that the geometries close to this phase transition might be manifold like.