Scientific Series

The study of isolated systems has been vastly successful in the context of vanishing cosmological constant, $\Lambda = 0$. However, there is no physically useful notion of asymptotics for the universe we inhabit with $\Lambda > 0$. The full non-linear framework is still under development, but some interesting results at the linearized level have been obtained. I will focus on the conceptual subtleties that arise at the linearized level and discuss the quadrupole formula for gravitational radiation.

A Coxeter category is a braided tensor category which carries an action of a generalised braid group $B_W$ on its objects. The axiomatics of a Coxeter category and the data defining the action of $B_W$ are similar in flavor to the associativity and commutativity constraints in a monoidal category, but arerelated to the coherence of a family of fiber functors.

We will show how to construct two examples of such structure on the integrable category $\matcal{O}$ representations of a symmetrisable Kac–Moody algebra $\mathfrak{g}$, the first one arising from the quantum group $U_\hbar(\mathfrak{g})$, and the second one encoding the monodromy of the KZ and Casimir connections of $\mathfrak{g}$.

The rigidity of this structure, proved in the framework of $\mathsf{PROP}$ categories, implies in particular that the monodromy of the Casimir connection is given by the quantum Weyl group operators of $U_\hbar(\mathfrak{g})$.

This is a joint work with Valerio Toledano Laredo.

In this talk, I will show how entropy perturbations created during a contracting phase and converted into adiabatic/curvature perturbations after a bounce form the dominant contribution to the observed temperature fluctuations in the CMB.
In [arXiv:1607.05663] we have studied two-field bouncing cosmologies in which primordial perturbations are created in either an ekpyrotic or a matter-dominated contraction phase. We then used a non-singular ghost condensate bounce model to follow the perturbations through the bounce into the expanding phase of the universe. In contrast to the adiabatic perturbations, which on large scales are conserved across the bounce, entropy perturbations can grow significantly during the bounce phase. If they are converted into adiabatic/curvature perturbations after the bounce, they typically form the dominant contribution to the observed temperature fluctuations in the microwave background, which can have several beneficial implications. For ekpyrotic models, this mechanism loosens the constraints on the amplitude of the ekpyrotic potential while naturally suppressing the intrinsic amount of non-Gaussianity. For matter bounce models, the mechanism amplifies the scalar perturbations compared to the associated primordial gravitational waves with the consequence that the tensor-to-scalar ratio is typically reduced by an order of magnitude or so, bringing it close to current observational bounds.

We reconsider a gauge theory of gravity in which the gauge group is the conformal group SO(4,2), and the action is of the Yang-Mills form, quadratic in the curvature. The vacuum sector of the resulting gravitational theory exhibits local conformal symmetry. We allow for conventional matter coupled to the spacetime metric as well as matter coupled to the field that gauges special conformal transformations.  When the theory is linearized about flat space, we find there is a long range gravitational force in addition to Newton’s inverse square law.  Furthermore, the cosmological sector of the theory exhibits late time acceleration, an early time bounce, and a post-bounce quasi-de Sitter ``inflationary'' phase of arbitrary duration (without an inflaton).

Dimer models have long been a fruitful playground for understanding topological physics. We introduce a new class -- termed Majorana-dimer models -- where the dimers represent pairs of Majorana modes. We find that the simplest examples of such systems realize an intriguing, intrinsically fermionic phase of matter that can be viewed as the product of a chiral Ising theory, which hosts deconfined non-Abelian Ising quasiparticles, and a topological (p − ip) superconductor. While the bulk anyons are described by a single copy of the Ising theory, the edge remains fully gapped. Consequently, this phase can arise in exactly solvable, frustration-free models. We present parent Hamiltonians for this phase and unambiguously identify the topological order from entanglement measurement of the ground-state manifold on torus.

Aretakis' discovery of a horizon instability of extremal black holes came as something of a surprise given earlier proofs that individual frequency modes are bounded. Is this kind of instability invisible to frequency-domain analysis? The answer is no: We show that the horizon instability can be recovered in a mode analysis as a branch point at the horizon frequency.  We use the approach to generalize to nonaxisymmetric gravitational perturbations and reveal that certain Weyl scalars are unbounded in time on the horizon.  We will also discuss new results showing how the instability manifests for *nearly* extremal black holes: long-lived quasinormal modes collectively give rise to a transient period of growth near the horizon.  This period lasts arbitrarily long in the extremal limit, reproducing the Aretakis instability precisely on the horizon.   We interpret these results in terms of near-horizon geometry and discuss potential astrophysical implications.

Quantum many-body systems are challenging to study because of their exponentially large Hilbert spaces, but at the same time they are an area for exciting new physics due to the effects of interactions between particles. For theoretical purposes, it is convenient to know if such systems can be expressed in a simpler way in terms of some nearly-free quasiparticles, or more generally if one can construct a large set of operators that approximately commute with the system’s Hamiltonian. In this talk I will discuss two ways of using the entanglement spectrum to tackle these questions. In the first part, I will show that strongly disordered systems in the many-body localized phase have a universal power-law structure in their entanglement spectra. This is a consequence of their local integrability, and distinguishes such states from typical ground states of gapped systems. In the second part, I will introduce a notion of “interaction distance” and show that the entanglement spectrum can be used to quantify “how far” an interacting ground state is from a free

(Gaussian) state. I will discuss some examples of quantum spin chains and outline a few future directions.

[1] M. Serbyn, A. Michailidis, D. Abanin, Z. Papic, arXiv:1605.05737.

[2] C. J. Turner, K. Meichanetzidis, Z. Papic, and J. K. Pachos, arXiv:1607.02679.

1. Beatrice Bonga, "Closed universes and the CMB",

Abstract:
Cosmic microwave background (CMB) observations put strong constraints on the spatial curvature via estimation of the parameter $\Omega_k$. This is done assuming a nearly scale-invariant primordial power spectrum. However, we found that the inflationary dynamics is modified due to the presence of spatial curvature leading to corrections to the primordial power spectrum. When evolved to the surface of last scattering, the resulting temperature anisotropy spectrum shows deficit of power at low multipoles ($\ell<20$). This may partially explain the observed $3 \sigma$ anomaly of power suppression for $\ell <30$. Since the curvature effects are limited to low multipoles, the estimation of cosmological parameters remains robust under inclusion of positive spatial curvature.

(This talk is based on http://arxiv.org/abs/1605.07556)

2. Keir Rogers, "Spin-SILC: CMB polarisation component separation for next-generation experiments",

Abstract:

B-mode polarisation is a powerful cosmological observable which in principle allows the detection of a stochastic background of gravitational waves predicted by inflation, and gives strong constraints on the neutrino sector using the weak gravitational lensing of the cosmic microwave background (CMB). Astrophysical foregrounds present a formidable obstacle in extracting these signatures of new physics from CMB polarisation data. Indeed, recent forecasts for post-2020 CMB experiments predict one sigma constraints on, for example, the tensor-to-scalar ratio of about 10^-4 and the sum of neutrino masses of about 30 meV. However, these constraints are predicated on highly-accurate foreground and noise removal. I will present the first component separation method specifically developed for this task and tested on the latest-release Planck data. The method, Spin-SILC, is an internal linear combination algorithm that uses spin wavelets to fully analyse the spin polarisation signal P = Q + iU, where Q and U are the measured Stokes parameters. This allows all the information in the measured signal to be used in extracting the cosmological background. Furthermore, Spin-SILC is the first method to simultaneously and efficiently perform component separation and the E-B decomposition necessary for cosmological analyses thanks to the construction of the spin wavelets we use. Spin-SILC also uses the morphological information of the foregrounds and CMB to better localise the cleaning algorithm. This is because the wavelets we use are additionally directional, and, when convolved with signals on the sphere, can separate the filamentary structures which are characteristic of both the CMB and foregrounds. I will present the results of applying these novelties to Planck data and discuss further how Spin-SILC can also mitigate the E-B leakage problem of future CMB experiments.

One dimensional symmetry protected topological (SPT) phases are gapped phases of matter whose edges are degenerate if the Hamiltonian respects a particular symmetry. With their interacting classification having been understood since 2010, we would like to further our understanding by addressing the following two questions: (1) Is there a unified way of understanding some of the exactly soluble models for 1D SPTs? And (2) if we are given two arbitrary SPTs, can we predict the structure of the phase transition between them? The answers turn out to be surprisingly simple. The first is given by relating various models to the Kitaev chain, uncovering new facts about some well-known SPTs. As for the transition between two arbitrary SPTs, it is generically described by a free conformal field theory which is determined by the topological class of the gapped phases.