Scientific Series

I will discuss how to classify (up to discrete identifications) all rigid 4D N=2 supersymmetric backgrounds in both Lorentzian and Euclidean signatures that preserve eight real supercharges. These include backgrounds such as warped S_3×R, warped AdS_3×R, and AdS_2×S^2, as well as some more exotic geometries. I will also address how to construct all supersymmetric two-derivative actions involving hypermultiplets and vector multiplets in these backgrounds.

We introduce the notion of a local shadow for a black hole and determine its shape for the particular case of a distorted Schwarzschild black hole. Considering the lowest-order  even and odd multiple moments, we compute the relation between the deformations of the shadow of a Schwarzschild black hole and the distortion multiple moments. For the range of values of multiple moments that we consider, the horizon is deformed much less than its corresponding shadow, suggesting the horizon is more `rigid'.  Quite unexpectedly we find that a prolate distortion of the horizon gives rise to an oblate distortion of the shadow, and vice-versa.

I’ll present new approaches to the problems of quantum control and quantum tomography wherein no classical simulation is required. The experiment itself performs the simulation (in situ) and, in a sense, guides itself to the correct solution. The algorithm is iterative and makes use of ideas from stochastic optimization theory.

Experiments and observations over the last decade and a half have persuaded cosmologists that (as yet undetected) dark energy is by far the main component of the energy budget of the universe. I review a few simple dark energy models and compare their predictions to observational data, to derive dark energy model-parameter constraints and to test consistency of different data sets. I conclude with a list of open cosmological questions.

I will discuss the appeal of pseudo-Goldstone bosons (pGBs) for the generation of scales in Early Universe cosmology. In particular, I will demonstrate how in Goldstone Inflation a pGB inflaton can solve the hierarchy problem of inflation (the tension between the Lyth bound and the inflationary scale as preferred by CMB anisotropies), while avoiding the problems with trans-Planckian scales that are typically associated with related models. A simple model based on the coset SU(4)/Sp(4) realises both the Higgs doublet and an inflaton singlet as Goldstone modes. A single setup can then give rise to Goldstone Inflation and the dynamical generation of the electroweak scale through a composite Higgs, thus also addressing the EW hierarchy problem. I will discuss perturbative reheating in this model, and show how it naturally connects to both EW physics and a UV completion. If time permits I will address our current studies on non-perturbative reheating and the possibility of electroweak baryogenesis in this setup. 

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.