The appearance of parity breaking in the electroweak sector, the notion of unification of fundamental forces, and the expectation that a deeper understanding of the Big Bang requires new physics all lead us to consider the search for cosmological signatures of parity breaking. I will review an array of parity-breaking signatures built from large-scale-structure and cosmic-microwave-background data and attempt to connect them models for new physics, most rooted on the inclusion of Chern-Simons terms in the Lagrangian.

With the advent of gravitational wave astronomy we are now in a perfect position to confront the multitude of beyond-GR theories, typically invoked to connect to quantum gravity paradigms, with actual observations in the strong-field regime of gravity. A necessary ingredient to do so, either via theory-specific tests or to inform parametrized approaches, are theoretical models describing the dynamics of compact binaries in extensions of general relativity. In this talk I will present recent results on modelling black hole binaries in scalar Gauss-Bonnet gravity, that involves higher-curvature corrections to Einstein's equations. As the parity-even cousin of dynamical Chern-Simons gravity, they share common features they may act as guide to phenomenology in dCS. For example, black holes can acquire scalar hair or spontaneously scalarize. Thus, binaries thereof yield new phenomena such as additional scalar radiation, dephasing of the gravitational wave signal and dynamical (de-)scalarization upon merger.

In this talk, I will introduce the perturbative and non-perturbative canonical quantization of gravity in the presence of a cosmological constant. I will review the advantages of the self-dual formulation of gravity and present the Chern-Simons states discovered by Kodama. I will discuss some successes and some puzzles associated with this state. I will present the construction of the physical scalar product, which provides a non-perturbative solution to the reality conditions and solve a long-standing puzzle. Finally, I will discuss some of the challenges that these results raise.

I review a recent approach to connecting quantum gravity and the real world by deconstantizing the constants of nature, and using their conjugate as a time variable. This is nothing but a generalization of unimodular gravity. The wave functions are then packets of plane waves moving in a space that generalizes the Chern-Simons functional. For appropriate states they link up with classical cosmology in the appropriate limit. There are however deviations, namely during the matter to Lambda transition, raising the possibility that quantum gravity could be in action here and now. At the other extreme I show how this approach can be used to resolve the cosmological singularity, and perhaps more.

This talk describes a continuation of the program of causal views, in which the world consists of nothing but a vast number of partial views of its past. Each view is associated to an event, and is a representation of the immediate causal past of that event. These consists mainly of processes that transfer energy, momentum and other charges to it from its past events.There is fundamentally no space or spacetime, just a large number of events, which are the causes of events to come.
We show that in a relativistic version of the theory a view of an event is represented by a quantum state. of a Chern-Simons on an N-punctured sphere. N is the number of immediate past events; the cosmological constant is related to the level by
k = 16 \pi /G \Lambda
Momentum and energy are fundamental, and are conserved under their transformation from present events to future events. As a result Minkowski spacetime emerges, in a way that preserves causal relations. The locality of events as constructed in the emergent spacetime is a consequence of the conservation of energy-momentum fundamentally.