Shape Dynamics Workshop
On the path towards quantum gravity we find friction between temporal relations in quantum mechanics (QM) (where they are fixed and field-independent), and in general relativity (where they are field-dependent and dynamic). In this talk, I will erase that distinction. I encode gravity, along with other types of interactions, in the timeless configuration space of spatial fields, with dynamics obtained through a path integral formulation. The framework demands that boundary conditions for this path integral be uniquely given.
I will present results on the quantization of an FRLW model that utilises a Schrodinger-type evolution equation. In contrast to standard Wheeler--DeWitt-type quantisations, the quantum model resolves the classical singularity, exhibits a quantum bounce, and displays novel early-universe phenomenology. A global scale emerges because of a scale anomaly, and suggests an interesting scenario for quantum shape dynamics. I will give the details of the quantization procedure and show how these techniques can be used more generally for anisotropic models.
I will with simple examples from spatially homogeneous and isotropic cosmology illustrate the importance of respecting the global features of a state space for a given model when reformulating field equations to useful dynamical systems. In particular I will use examples from f(R) gravity and GR with a minimally coupled scalar field.
I will show how the intrinsic definition of observables in relativity through dynamical similiarity (known as Shape Dynamics) leads to the continuation of Einstein's equations classically through the big bang singularity in simple cosmological scenarios. By appealing to general principles I argue that this is a generic feature, and that the singularity can be viewed as an artifact of the redundant description imposed by absolute length scales.
I will discuss various ways of realizing the Weyl group in a theory of gravity, and the presence or absence of anomalies.
I will discuss the use of (functional) Renormalization Group in models of quantum gravity. I will highlight the challenges that occur in continuum approaches to quantum gravity, such as asymptotically safe gravity, as well as challenges in discrete approaches, such as tensor models.
I review motivations for a frame-dependent dark energy action proportional to $\int d^4x (-g)^{1/2}/g_{00}^2$, and discuss implications for the black hole horizon and for perturbations on the Robertson-Walker line element.
The Weyl Theorem states that the conformal structure and the projective structure jointly suffice to fix the metric up to a global constant. This is a powerful interpretive tool in general relativity: it says in effect that if I know the paths of light rays in vacuo and I know the images of the paths of freely falling particles (i.e., the spacetime curves they follow with no preferred parametrization), then I know the metric.