Scientific Series

I describe an inflation model that can generate a cosmological magnetic seed field of nG strength on Mpc length scales today that could explain observed few microG large-scale galactic magnetic fields. I also summarize some of the extensions of this model that have been developed over the last two decades, as well as open questions about such models.

The kinematical framework of canonical loop quantum gravity has mostly been studied in the context of compact Cauchy slices. However many key physical notions such as total energy and momentum require the use of asymptotically flat boundary conditions (and hence non-compact slices). We present a quantum kinematics, based on the Koslowski-Sahlmann representation, that successfully incorporates such asymptotically flat boundary conditions. Based on joint work with Madhavan Varadarajan.

The continued lack of definitive signals at direct detection experiments places many models of weakly interacting dark matter into tension. Direct detection is naturally suppressed in models where the dark matter co-annihilates with another particle in the early universe.  The cosmology, direct detection, and LHC signals of such models can often be well understood by considering only the most relevant low-energy degrees of freedom.  We draw lessons for the Minimal Supersymmetric Standard Model.

The Lagrangian dynamics of a fluid element within a self-gravitational matter field is intrinsically nonlocal due to the presence of the tidal force. Instead of searching for local approximations, we provide a statistical solution that could decouple the evolution of the fluid parcel from the surrounding environment. Given the probability distribution of the matter field, the method produces a set of ordinary differential equations to be solved locally. Mathematically, it corresponds to the characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Physically, it describes the mean evolution of the element with specific density and shape averaged over various environments. Furthermore, it is guaranteed that the one-point ρPDF would be preserved if one evolves these local, yet nonlinear, curves with the same set of initial data as the real system. This PDF based method, which is well developed in turbulence and other fields, provides a new perspective for understanding the non-linear structure formation in cosmology, e.g. the halo formation and the evolution of cosmic web. For Gaussian distributed dynamical variables, we demonstrate that the localized mean tidal tensor is proportional to the shear tensor, and the coefficient would recover the prediction of Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For Weakly non-Gaussian field, the averaged tidal tensor could then be expressed as polynomial of other variables.  Moreover, one could further generalize this concept of the mean evolution of the fluid element to incorporate some stochastic contributions, which we suggest would be valuable in describing a variety of processes in cosmology, such as the shell-crossing and realistic halo formation.

I will describe a proposal for a generalization of the BMS group in which the conformal isometries of the sphere (Lorentz group) are replaced by arbitrary sphere diffeomorphisms. I describe the computation of canonical charges and show that the associated Ward identities are equivalent to the Cachazo-Strominger subleading soft graviton formula. Based on joint work with Alok Laddha.

Scalar fields are a useful proxy for other complex interactions, but also an attractive extension of General Relativity and a possible dark matter component. I will discuss some aspects of the gravitational interaction of scalar fields, in particular (i) the formation and growth of self-gravitating structures and their interaction with compact stars. and (ii) superradiance around black holes and how it can be used to constraint particle masses.

A new analysis of electron-proton scattering data (those published in 2010 by the Mainz A1 collaboration and previous world compilations) to determine the proton electric and magnetic radii is presented. The analysis enforces model-independent constraints of form factor analyticity and investigates a wide range of possible systematic effects. Employing standard models for radiative corrections, our improved analysis yields proton electric radii for the Mainz and world data sets that are consistent, although a simple combination yields a value r_E = 0.904(15) fm that is 4-sigma larger than the CREMA muonic hydrogen determination. Remaining possible deficiencies are discussed that, if addressed, could reconcile the values from muonic hydrogen spectroscopy and ep-scattering.

In this talk I’ll discuss an exotic theory of gravity known as “partially massless” gravity.  The linear partially massless theory displays many features analogous to those of electromagnetism, including an electric/magnetic duality.  However, the structure of gauge charges is much richer than in E&M.  I’ll present the analogues of electric point charges and Dirac monopoles.

An algebraic view allows one to compute properties of physical states without having to introduce an explicit Hilbert space. In relational systems without absolute time, a state cannot be completely positive once a choice for a (possibly local) internal time has been made. A more general class of `almost-positive' states is introduced in this talk, together with a discussion of their constrained dynamics.

We hope to find clues about the particle physics of the primordial (inflationary?) universe in the statistics of the cosmological perturbations. However, if the fluctuations are non-Gaussian the statistics we observe can differ significantly from the global, mean predictions of an inflationary model. I will discuss how the conclusions we draw about the primordial degrees of freedom can be affected in interesting ways by the finiteness of our observable universe.

After a short review of the gauge gravity duality, we will discuss black holes.  We will explain what the duality tells us about black holes as viewed from the outside.  We will review some of the puzzles that arise when we try to describe the black hole  interior. We will describe wormholes and their interpretation in the dual field theory as entangled states.

Matrix product operators form a natural language for describing topological quantum order. I will discuss how they arise as symmetries in PEPS, how anyon excitations arise as end points on them, and how the virtual indices of the MPO's provide a tensor product structure for the logical qubits in topological quantum computation.