Scientific Series

The standard cosmological model features two periods of accelerated expansion: an inflationary epoch at early times, and a dark energy dominated epoch at late times. These periods of accelerated expansion can lead to surprisingly strong constraints on models with extra dimensions. I will describe new mathematical results which enable one to reconstruct features of a higher-dimensional theory based on the behaviour of the accelerating four-dimensional cosmology. When applied to inflation, these results pose several interesting questions for the construction of concrete models. When applied to dark energy, they provide a new technique to combine measurements of dark energy parameters and constraints on variation of Newton's constant. This technique can transform near-future dark energy surveys into become powerful probes of extra dimensional physics.

Weak lensing has emerged as a powerful probe of fundamental physics such as dark energy and dark matter. After briefly reviewing the standard argument for the power of lensing, I present a variety of surprises: some quantities that are supposedly simple measures of cosmic shear are actually polluted by other effects and some quantities apparently unrelated to lensing are contaminated by lensing. These effects may lead to opportunities to strengthen the constraints lensing will place on dark energy.

If Dark Energy is dynamical, it would indicate the existence of new physics beyond the standard model coupled to gravity. I will argue that the best motivated models of this new physics are all tied to whatever resolves the cosmological constant problem, and discuss the cosmological implications of several proposals that have been put forward in this vein.

A simple model for chaotic inflation in supergravity is proposed. The model is N = 1 supersymmetric massive U(1)gauge theory via the Stuckelberg superfield and gives rise to D-term inflation with a quadratic term of inflaton in the potential. The Fayet-Iliopoulos field plays a role of the inflaton. It is also discussed to give rise to successful reheating and leptogenesis through the inflaton decay.

I will present three ideas about black holes and cosmology. First, I will discuss a way of understanding the simple patterns which emerge from the notoriously thorny numerical simulations of binary black hole merger, and some of the directions where this understanding may lead. Second, I will suggest a sequence of practical bootstrap tests designed to give sharp observational confirmation of the essential idea underlying the inflationary paradigm: that the universe underwent a period of accelerated expansion followed by a long period of decelerated expansion. Third, I will investigate a way that one might try to detect the strong bending of light rays in the vicinity of a black hole.

Eugene Wigner and Hermann Weyl led the way in applying the theory of group representations to the newly formulated theory of quantum mechanics starting in 1927. My talk will focus, first, on two aspects of this early work. Physicists had long exploited symmetries as a way of simplifying problems within classical physics. Wigner recognized that the theory of group representations would similarly have enormous payoff in quantum mechanics, allowing him to solve problems in atomic spectroscopy ``almost without calculation.'' Here I will describe the novel aspects of symmetry in QM that Wigner clarified in the series of papers leading up to his 1931 textbook (Wigner's theorem, projective representations, etc.). The second aspect is less well-known: Weyl (1927) argued that group theory could also be used to address foundational questions in quantum mechanics, leading to a reformulation of the classical commutation relations and a proposal for quantization. Weyl's program had much less immediate impact, although it led to the Stone-von Neumann theorem and to Mackey's imprimitivity theorem. As a final historical point, I argue that in this early work the theory of group representations was optional (as emphasized by Slater and others) in a sense that it was not in particle physics in the 60s. The closing section of the talk turns to philosophical morals that have been drawn from this historical episode, in particular claims regarding ontic structural realism (French, Ladyman) and the group-theoretic constitution of objects (Castellani).

Quantum graphity is a background independent condensed matter model for emergent locality, spatial geometry and matter in quantum gravity. The states of the system are given by bosonic degrees of freedom on a dynamical graph on N vertices. At high energy, the graph is the complete graph on N vertices and the physics is invariant under the full symmetric group acting on the vertices and highly non-local. The ground state dynamically breaks the permutation symmetry to translations and rotations. In this phase the system is ordered, low-dimensional and local. The model gives rise to an emergent U(1) gauge theory in the ground state by the string-net condensation mechanism of Levin and Wen. In addition, in such a model, observable effects of emergent locality such as its imprint on the CMB can be studied. Finding the right dynamics for the desired ground state is ongoing work and I will review some of the basic results with an emphasis on the use of methods from quantum information theory such as topological order and the use of the Lieb-Robinson bounds to find the speed of light in the system.

Quantum foundations in the light of gauge theories We will present the conjecture according to which the fact that q and p cannot be both ``observables'' of the same quantum system indicates that there is a remnant universal symmetry acting on classical states. In order to unpack this claim we will generalize to unconstrained systems the gauge correspondence between properties defined by first-class constraints and gauge symmetries generated by these constraints. As we shall see, this means that the uncertainty principle might be encoded in the very definition of the canonical variables q and p. According to the ontology of quantum objects that stems from this analysis, the quantum-mechanical description of physical objects is complete.

I will revisit the phenomenology of the radion graviscalar in warped extra dimensions. This particle could be the lightest 'new physics' state to be discovered at the LHC in this type of models. Its phenomenology is very similar to the Standard Model (SM) Higgs, another potentially light scalar particle with which it could actually mix. When SM fields are moved from the boundary to the bulk of the extra dimension, new interesting effects appear in the scalar sector of the model. With a little bit of Higgs-radion mixing, it is possible to enhance importantly some decay channels of the mostly-radion scalar. Moreover, both the Higgs and the radion can now typically mediate Flavor Changing Neutral Currents at tree level. These will impose bounds on the flavor structure of the model, but also allow for interesting probes in current and future collider experiments.

The Rozansky-Witten model is a topological sigma-model in three dimensions whose target is a hyper-Kahler manifold. Upon compactification to 2d it reduces to the B-model with the same target. Boundary conditions for the Rozansky-Witten model can be regarded as a 3d generalization of B-branes. While branes form a category, boundary conditions in a 3d TFT form a 2-category. I will describe the structure of this 2-category for the Rozansky-Witten model and its connection with a categorification of deformation quantization. I will also discuss defects of codimension 1 (domain walls) and defects of codimension 2 (line operators) in the Rozansky-Witten model.

In topological quantum computation the geometric details of a particle trajectory become irrelevant; only the topology matters. This is one reason for the inherent fault tolerance of topological quantum computation. I will speak about a model in which this idea is taken one step further. Even the topology is irrelevant. The computation is determined solely by the permutation of the particles. Unlike topological quantum computation, which requires anyons confined to two dimensions, permutational quantum computations can in principle be performed by permuting a set of ordinary spin-1/2 particles with definite total angular momentum in three dimensions. The resulting model of computation appears to be intermediate in power between classical computation (P) and standard quantum computation (BQP). The model may be equivalently defined in terms of spin networks, which are an important concept in loop quantum gravity.

Quantum mechanics is a non-classical probability theory, but hardly the most general one imaginable: any compact convex set can serve as the state space for an abstract probabilistic model (classical models corresponding to simplices). From this altitude, one sees that many phenomena commonly regarded as ``characteristically quantum' are in fact generically ``non-classical'. In this talk, I'll show that almost any non-classical probabilistic theory shares with quantum mechanics a notion of entanglement and, with this, a version of the so-called measurement problem. I'll then discuss what's required for an abstract probabilistic theory to admit a somewhat simplified version of Everett's response to this problem -- an exercise that turns out to be instructive in several ways.