Beyond Part III

Young Researchers in Mathematics 2009

16-18 April 2009

Centre for Mathematical Sciences, Cambridge

General Relativity/Cosmology Session

Talks will be in the Pavillion B common room.



The domain of dependence property and wave equations in relativity - Jacques Smulevici

The domain of dependence property is one of the fundamental properties of the wave equation on Minkowski space, and more generally, of geometric hyperbolic wave equations. Physically, it corresponds to a finite speed of propagation. It has deep consequences, both from the point of view of physics and mathematics. In particular, the domain of dependence property will lead us to postulate the strong cosmic censorship, one of the main conjecture of general relativity.

Strong cosmic censorship for solutions of the Einstein-Maxwell equations with polarized Gowdy symmetry - Ernesto Nungesser

Some results on the proof of strong cosmic censorship are presented for a class of solutions of the Einstein-Maxwell equations, those with polarized Gowdy symmetry. A key element of the argument is the observation that by means of a suitable choice of variables the central equations in this problem can be written in a form where they are identical to the central equations for general (i.e. non-polarized) vacuum Gowdy spacetimes. Using this it is seen that the deep results of Ringstroem on strong cosmic censorship in the vacuum case have implications for the Einstein-Maxwell case. Working out the geometrical meaning of these analytical results leads to the main conclusion.

Higher dimensional black holes - Harvey Reall (keynote speaker)

Black holes in more than four spacetime dimensions exhibit much richer behaviour than in four dimensions. The properties of higher-dimensional black holes will be reviewed and the implications for string theory discussed.

Dark Energy in the Early Universe - Joel Weller

It is well known that the dynamics of the universe in recent times depends on the properties of dark energy and dark matter. In this talk I will explore the consequences of a coupling between these components by considering a model in which dark energy plays an important role in the early universe. By considering the physics of the inflationary era and during reheating, I will show how the presence of the coupling modifies the standard results.

Effect of the Trace Anomaly on the Cosmological Constant - Jurjen Koksma

It has been argued that the quantum (conformal) trace anomaly could potentially provide us with a dynamical explanation of the cosmological constant problem. In this talk, however, we show by means of a semiclassical analysis that the trace anomaly does not affect the cosmological constant. We calculate the evolution of the Hubble parameter in quasi de Sitter spacetime, where we restrict our Hubble parameter to vary slowly in time, and in FLRW spacetimes. We show dynamically that a Universe consisting of matter with a constant equation of state, a cosmological constant and the quantum trace anomaly evolves either to the classical de Sitter attractor or to a quantum trace anomaly driven one. Semiclassically, the trace anomaly does not affect the classical late time de Sitter attractor and hence it does not solve the cosmological constant problem.

Curvaton model in the Very Early Universe - Jose Fonseca

In the past few years observational data has been extremely helpful to probe the primordial universe. More recently, hints for non-gaussianity in the distribution of primordial density perturbations has been found. Such a discovery would require major revision of the standard model of inflation in the very early universe. A candidate to explain either the power spectrum and the non-gaussianity is the Curvaton Model. I will review the latest results from WMAP Satellite. Then i will take a look to the basic ideas of Inflation. Then I will introduce the basis of the Curvaton Scenario and review its predicted power spectrum as well as the expected non-gaussianity. Finally I will introduce the work that I have been carrying out in the Curvaton Model.

Causal Set Theory - Lydia Philpott

Is spacetime a discrete or continuous structure? I will briefly review causal set theory, a Lorentz invariant discrete approach to quantum gravity, and then discuss how discreteness could affect particle behaviour. Particles propagating in a fundamentally discrete spacetime will not follow the smooth geodesics predicted by GR. Motivated by causal set theory we can develop phenomenological models for such particles. On macroscopic scales the particles will undergo a diffusion in momentum. Comparison with observation allows us to place tight constraints on the free parameters in the model.

Cosmic Superstrings: dynamics and cusps - William Nelson

Cosmic strings form in field theories when there are topological obstructions to reaching the true vaccum. It is well known that on loops of such Cosmic Strings, points of luminous velocity generical form. I will describe how this happens and briefly mention what the consequences of this are, before describing how things change when we consider Cosmic Superstrings. These string theory objects are expected to have formed at the end of brane inflation and if they were to be observed and distinugished from standard Cosmic Strings, they could open up an important observational window into low-energy string theory and string inflation.

Hidden Symmetries of Black Rings - Mark Durkee

In the last couple of years there has been much progress in constructing new exact vacuum black holes in five dimensions; but many of the resulting metrics are very complicated. In this talk I discuss the Pomeransky-Sen'kov doubly-spinning black ring, probably the most general connected black ring in 5D. I will show that it possesses an unexpected amount of hidden symmetry that allows the geodesic equation to be solved analytically in certain cases, with the resulting null geodesics having applications in constructing new coordinates systems that are valid across the event horizon.