Talks

Dark energy, the driver of the accelerated expansion of the universe, remains a conundrum. New physics may well be needed to explain it; from Lorentz invariance, this new physics should contain scalar fields, which should be straightforward to detect — so where are they? Physicists have now realized that scalar fields can hide from detection by three distinct screening mechanisms, which respectively rely on nonlinear features in the scalar’s kinetic energy, potential energy, or coupling to normal matter. These fields go by names such as galileons, chameleons, f(R) gravity, or symmetrons and range from theoretically well-motivated and natural to speculative. We will present new techniques to detect these particles, relying on interferometry with cold atoms in vacuum. The low density of such atoms compared to bulk matter avoids triggering some screening mechanisms, while the high sensitivity of the interferometer overcomes other screening mechanisms by brute force. We will show limits ruling out substantial regions of parameter space for chameleons and symmetrons [Science 349, 849 (2015)] and argue that an interferometer with 10,000 fold improved sensitivity will be able to search the gamut of screened scalar fields. A positive identification would revolutionize particle physics and cosmology, but even a null result would have important implications for our understanding of the dark sector. 

In the coming decade, ground based CMB telescopes could face a substantial upgrade, to so-called CMB-S4. There are two main science drivers behind this initiative: B-modes, and neutrino mass, and I will focus on the latter. Thought of more generally, constraints on neutrinos can be thought of as generic tests of dark matter. I will discuss the prospects for CMB-S4 in the dark sector, with emphasis on searches for axions and neutrinos. It will be possible to detect percent level departures from standard cold dark matter at many sigma over a wide range of scales: a vast improvement over Planck (+ existing ground based). A large part of the improvement over Planck comes from precision lensing measurements at high multipole. I will briefly discuss some technical challenges in this measurement, based on modelling of dark matter clustering in the non-linear regime.

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.