Conference

In two dimensional CFTs the Zamolodchikov\'s c-theorem is fundamental in that it shows that the number of degrees of freedom decreases along the renormalization group flow. I will give a short history of and discuss recent developments in the quest to find its four-dimensional analogue using the central charges a & c.

There is an ongoing debate in the literature concerning the effects of averaging out inhomogeneities (``backreaction\'\') in cosmology. In particular, it has been suggested that the backreaction can play a significant role at late times, and that the standard perturbed FLRW framework is no longer a good approximation during structure formation, when the density contrast becomes nonlinear. After a brief introduction to the problem, I will show using Zalaletdinov\'s covariantaveraging scheme that as long as the metric of the universe can be described by the perturbed FLRW form, the corrections due to averaging remain negligibly small. Further, using a fully relativistic and reasonably generic model of pressureless spherical collapse, I will show that as long as matter velocities remain small (which is true in this model even at late times), the perturbed FLRW form of the metric can be explicitly recovered. Together with the observation that real peculiar velocities are in fact nonrelativistic, these results imply that the backreaction remains small even during nonlinear structure formation.

Non-Gaussianity is a powerful observable that may reveal important properties of the fundamental physics of inflation, with qualitative and quantitative features of higher order correlation functions distinguishing between models. Here I will discuss the structure of correlation functions in the most general single field inflation model and explain why this information is important for making use of observations from the CMB and large scale structure.

Despite over 40 years of research on Bell-type inequalities and the question of non-locality, new technical results that have general foundational relevance can still be obtained. In this talk will present a number of new results that deal with the question of how to discern local, quantum and no-signaling correlations. • 1) I will present a non-trivial no-signaling inequality that discerns no-signaling correlations from general correlations - the first to our knowledge. This inequality has a striking similarity with the CHSH inequality, yet it is crucially different. • 2) I will next discuss interesting relationships that can be inferred between some well-known conditions at different hidden- variable levels (such as the assumptions of outcome and parameter independence). The upshot of the analysis will be that which conditions are to be obeyed by different kinds of correlations and which are not, depends on the level of consideration. A conclusive picture therefore depends on which hidden-variable level is considered to be fundamental. • 3) I will further comment on interesting relationships that exist between inferences on the surface and subsurface level. Here the surface level deals with experimentally accessible probabilities (e.g., via relative frequencies) and the sub-surface level deals with probabilities that are conditioned on a hidden-variable (or the quantum state). The most interesting such a relationship is the following: any deterministic hidden-variable theory that obeys no- signaling and gives non-local correlations must show randomness at the surface, i.e., the surface probabilities cannot be deterministic. This is the case in Bohmian mechanics but this result shows it to be generic. Throughout the talk I will show how these three topics are related, and comment on the foundational impact of the results obtained.

The efficient computation of scattering amplitudes in quantum field theory has many important applications, ranging from the computation of QCD backgrounds at the LHC to the study of the perturbative finiteness of N=8 supergravity. \'On-shell methods\' are a crucial ingredient in the computation of gauge theory and gravity amplitudes because they are far more efficient than traditional Feynman diagram techniques. I give an introduction to the basic concepts used in this field. I explain one particularly elegant method, the MHV vertex expansion, and outline how we recently proved the validity of this expansion in N=4 Super Yang-Mills Theory.

I discuss our recent investigations into 2+1 dim Chern-Simons theories with gravity duals that have reduced supersymmetry. Many new phenomena such as fractional statistics arise in 2+1 dim field theory that make this duality interesting and subtle. I focus on our work involving an example of such a duality with minimal supersymmetry and propose a field theoretic dual for a long known vacuum of gauged supergravity on AdS_4. I also argue that 2+1 dim duality might present a favorable landscape for constructing non-supersymmetric conformal fixed points at large but finite N.

One of the most challenging problems in theoretical physics today is the so called cosmological constant problem. While current observations are consistent with the prediction of GR with an unexplainable tiny cosmological constant, it remains possible that it\'s the deviation of the law of gravity at large distance from Einstein\'s theory that resolves the puzzle. In this talk, I will briefly review some of the theoretical attempts we made along this line, in particular, the so called \'classically constrained gravity\' and its implications in quantum cosmology. I will also present some most recent study on massive spin-2 particles in De Sitter space, and describe a model, initially motivated by DGP theory, which allows one to explore the Higuchi forbidden mass range of the graviton on the De Sitter background.

WMAP measurements of CMB temperature anisotropies reveal a power asymmetry: the average amplitude of temperature fluctuations in one hemisphere is larger than the average amplitude in the opposite hemisphere at the 99% confidence level. This power asymmetry may be generated during inflation by a large-amplitude superhorizon perturbation that causes the mean energy density to vary across the observable Universe. Such a superhorizon perturbation would also induce large-scale temperature anisotropies in the CMB; measurements of the CMB quadrupole and octupole (but not the dipole!) therefore constrain the perturbation\'s amplitude and wavelength. I will show how a superhorizon perturbation in a multi-field inflationary theory, the curvaton model, can produce the observed power asymmetry without generating unacceptable temperature fluctuations in the CMB. I will also discuss how this mechanism for generating the power asymmetry will be tested by forthcoming CMB experiments.

Instead of adding another dark component to the energy budget of the Universe in trying to explain the accelerated expansion, one can ask whether the cause is in fact the laws of gravity itself on the largest scales. In this talk, I will consider a sub-class of so-called f(R) gravity theories which closely follow the LambdaCDM expansion history, while at the same time evading tight Solar System constraints on gravity. I will present new results from cosmological N-body simulations which consistently solve for the modified gravitational force. In particular, I will discuss the effects of modified gravity on structure formation, dark matter halo properties, and cosmological observables.