General Relativity & Quantum Cosmology

Various self-similar spherically symmetric spacetimes admit naked singularities, providing a challenge to the cosmic censorship hypothesis. However, it is not clear if the naked singularities are artefacts of the high degree of symmetry of the spacetimes, or if they are potentially generically present. To address this question, we consider perturbations of (various cases of) these spacetimes, focusing particularly on the behaviour of the perturbations as they impinge on the Cauchy horizon. We describe recent results on self-similar Lemaitre-Tolman-Bondi spacetime, indicating stability of scalar and odd parity perturbations, and instability of even parity perturbations.

The effective field theory framework yields a systematic treatment of gravitational bound states such as binary systems. Gravitational waves emitted from compact binaries are one of the prime event candidates at direct detection experiments. Due to the multiple scales involved in the binary problem, an effective field theory treatment yields many advantages in perturbative calculations. My talk will review the setup of the effective field theory framework and report on recent progress in gravitational wave phenomenology.

The local and global properties of the retarded and Feynman Green functions to the wave equation in curved spacetime are crucial for radiation reaction in the classical theory and for renormalisation in the quantum quantum theory. Building on an insight due to Avramidi, we provide a system of transport equations for determining key fundamental geometrical bitensors determining the local Hadamard singularity structure of these Green’s functions. We illustrate their use in a semi-recursive approach showing how to determine covariant expansions to high order, for example, calculating the tail term reflecting backscattering by the curvature of spacetime to 20th order in the geodesic separation in a matter of minutes, and as the basis of numerical calculations. We also present an efficient method to construct covariant expansions of the tail term, without using the formal Hadamard light-cone expansion. Finally we discuss the relationship between the geodesic structure, quasi-normal modes with associated excitation factors and the global behaviour of Green functions in black hole space-times.

The standard method to study nonperturbative properties of quantum field theories is to Wick rotate the theory to Euclidean space and regulate it on a Euclidean Lattice. An alternative is "fuzzy field theory". This involves replacing the lattice field theory by a matrix model that approximates the field theory of interest, with the approximation becoming better as the matrix size is increased. The regulated field theory is one on a background noncommutative space. I will describe how this method works and present recent progress and surprises.

The upcoming launch of the space-based gravitational wave interferometer detector LISA will yield an unprecedented amount of astrophysical and cosmological science from a variety of gravitational wave sources. Among these, the extreme mass ratio inspirals (EMRIs) of stellar-mass compact objects into supermassive black holes will provide a unique opportunity to test the predictions of General Relativity for strongly gravitating systems since the masses and spins of these sources are expected to be measured with precisions better than about 1 part in 10^4. Such highly precise measurements require modeling the dynamics of EMRIs and their gravitational waves with high accuracy. In this talk, I discuss using methods of effective field theory (EFT) to accomplish this. Since EMRIs lose energy to gravitational waves, I introduce an open systems framework that proves to be a necessary ingredient to correctly describe EMRIs within the EFT formalism. I will discuss my recent derivation of the equations of motion and waveforms through third order in the mass ratio for a class of nonlinear scalar models that are analogous to the perturbative General Relativistic description of EMRIs. Time permitting, I will also discuss new results that are non-perturbative in the mass ratio in this model.

Usually in quantum field theory one considers two different interpretations: 1: The field is an infinite number of quantum oscillators, giving rise to a wave functional \Psi(\phi). 2: The positive frequency component of a field, \phi_+(x), is a wave function analogous to standard quantum mechanics. While interpretation 2 is often only mentioned implicitly it is crucial to standard computations of measurable scattering probabilities. We extend the interpretation of QFT as relativistic quantum mechanics (option 2) and show how the total Klein Gordon field which consists of positive and negative frequency contributions, \phi = \phi_+ + \phi_- , can be interpreted as a wave function. Our construction manifestly shows that signal propagation in QFT cannot exceed the speed of light. This follows from the replacement of the Feynman propagator by the Wheeler propagator, which is just the time ordered commutator. Our second observation is that interpretation 2 is not consistent if one uses the Newton Wigner position operator, therefore we introduce a more natural bilinear position operator. We show by an explicit example that the bilinear operator, contrary to the Newton Wigner operator, allows relativistic particles to be perfectly localized, precisely as in non relativistic quantum mechanics.

We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or four-manifold as a branched cover. These data are expressed as monodromies, in a way similar to the encoding of the gravitational field via holonomies. We then describe convolution algebras of spin networks and spin foams, based on the different ways in which the same topology can be realized as a branched covering via covering moves, and on possible composition operations on spin foams. We illustrate the case of the groupoid algebra of the equivalence relation determined by covering moves and a 2-semigroupoid algebra arising from a 2-category of spin foams with composition operations corresponding to a fibered product of the branched coverings and the gluing of cobordisms. The spin foam amplitudes then give rise to dynamical flows on these algebras, and the existence of low temperature equilibrium states of Gibbs form is related to questions on the existence of topological invariants of embedded graphs and embedded two-complexes with given properties. We end by sketching a possible approach to combining the spin network and spin foam formalism with matter within the framework of spectral triples in noncommutative geometry. (Based on joint work with Domenic Denicola and Ahmad Zainy al-Yasry)

Several current experiments probe physics in the approximation in which Planck's constant and Newton's constant may be neglected, but, the Planck mass, is relevant. These include tests of the symmetry of the ground state of quantum gravity such as time delays in photons of different energies from gamma ray bursts. I will describe a new approach to quantum gravity phenomenology in this regime, developed with Giovanni Amelino-Camelia, Jersy Kowalski-Glikman and Laurent Freidel. This approach is based on a deepening of the relativity principle, according to which the invariant arena for non-quantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by observers, but different observers, separated from each other by translations, construct different spacetime projections from the invariant phase space. Nonetheless, all observers agree that interactions are local in the spacetime coordinates constructed by observers local to them. This framework, in which absolute locality is replaced by relative locality, results from deforming momentum space, just as the passage from absolute to relative simultaneity results from deforming the linear addition of velocities. Different aspects of momentum space geometry, such as its curvature, torsion and non-metricity, are reflected in different kinds of deformations of the energy-momentum conservation laws. These are in principle all measurable by appropriate experiments.

Assuming exotic matter, several models representing static, spherically symmetric wormhole solutions of Einstein's field equations have been considered in the literature. We examine the dynamical stability of such wormholes in one of the simplest model, in which the matter is described by a massless ghost scalar field, and prove that all solutions are unstable with respect to linear fluctuations and possess precisely one unstable, exponentially in time growing mode. Numerical simulations of the nonlinear field equations suggest that these wormholes either expand or collapse and form a black hole. The stability problem for alternative models including electrically charged wormholes is also discussed.

How many interacting quantum (field) theories of four-dimensional geometry are there which have General Relativity as their classical limit? Some of us still harbour hopes that a quantum theory of gravity is "reasonably unique", i.e. characterized by a finite number of free parameters. One framework in which such universality may manifest itself is that of "Quantum Gravity from Causal Dynamical Triangulations (CDT)". I will summarize the rationale behind this nonperturbative formulation and CDT's main achievements in trying to explain the micro- and macro-structure of spacetime from first principles. This includes the remarkable property of "dynamical reduction" of the spacetime dimension from four to two at the Planck scale.

The long awaited discovery of the double radio pulsar system, PSR J0737-3039A/B, surpassed most expectations, both theoretical and observational, as a tool to probe general relativity, stellar evolution and pulsar theories. The Double Pulsar provides a unique and the most complete and clean test of theories of gravity in a regime sensitive to possible strong-gravitational self-field effects. All six post-Keplerian parameters have been measured (including the measurement of the relativistic spin precession), some parameters to a precision of 10^{-4}.

NANOGrav is a consortium of radio astronomers and gravitational wave physicists whose goal is to detect gravitational waves using an array of millisecond pulsars as clocks. Whereas interferometric gravitational wave experiments use lasers to create the long arms of the detector, NANOGrav uses earth-pulsar pairs. The limits that pulsar timing places on the energy density of gravitational waves in the universe are on the brink of limiting models of galaxy formation and have already placed limits on the tension of cosmic strings. Pulsar timing has traditionally focused on stochastic sources, but most recently I have been investigating the idea of detecting individual gravitational wave bursts wherein there are some interesting advantages. I will also demonstrate how the array can be used to reconstruct the waveform and obtain its direction.