**Stephen Adler**, Institute for Advanced Study

*Implications of a Frame-Dependent Dark Energy Action*

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.

**Julian Barbour**, University of Oxford

*Shape Dynamics: Perspectives and Problems*

Shape Dynamics(SD) can be derived from principles that differ in significant respects from Einstein's derivation of GR. It requires a spatially closed universe and allows a smaller set of solutions than GR does for this case. There are indications that its solution space can be fully characterized and endowed with a measure. These architectonic features suggest that SD can explain the arrows of time as direct consequences of the law of the universe. They do not require special initial conditions. I will discuss these and other major issues on which SD may cast light. I will also discuss the problems that face SD.

**Yuri Bonder, **UNAM

*Relationalism and the speed of light: Are we in a relationship?*

Most practical studies in Shape Dynamics involve an N-body Newtonian interaction which is described by a homogeneous potential. This property allows one to proof several interesting features like the emergence of an arrow of time. However, more generic interactions are not described by these kind of potentials and introduce additional dimensionful coupling constants. Thus, it is an open question whether more generic interactions can be written in a fully relational manner. By studying the concrete example of the gravitational Weber interaction which is, in a sense, a more realistic theory of gravity, we show that it is possible translate non-Newtonian interactions, which have inhomogeneous potentials and additional coupling constants, into a relational language. This opens the door to study other interactions and may shed light into the relationalization of gravity as described by general relativity.

**Astrid Eichhorn**, University of Heidelberg

*Renormalization Group flows of spacetime*

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.

**Sean Gryb, **University of Bristol

*Quantum singularity resolution in homogeneous cosmology and the implications for shape dynamics*

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 end by speculating about how these techniques might be applicable to a genuine quantum shape model of the universe.

**James Isenberg**, University of Oregon

*What we know and don’t know about solutions to the Einstein Constraint Equations*

**Tim Koslowski**, UNAM

*The quantum equation of state of the universe produces a small cosmological constant*

Relationalism is the strict disentanglement of physical law from the definition of physical object. This can be formalized in the shape dynamcis postulate that the objective evolution of the universe is described by an "equation of state of a curve in relational configuration space." The application of this postulate to General Relativity implies that gravity is described by an equation of state of a curve on conformal superspace. It turns out that the naive quantization of these equations of state introduces an undesired preferred time parametrization. However, it turns out that one can still describe the quantum evolution of the system as an equation of state of the Bohmian trajectory which remains manifestly parametrization independent. These quantum systems generically develop quasi-isolated bound states (atoms) that can be used as reference systems. It turns out that the system as a whole expands if described in units defined by these atoms. This produces phenomenological effects that are usually ascribed to the presence of a cosmological constant. This "effective cosmological constant" is however unaffected by vacuum energy. I pesent the formal argument for this statement and show this explicitly by remormalizing a scalar field coupled to shape dynamics.

**Claes Uggla**, Karlstad University

*Dynamical systems approaches and methods in cosmology*

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. In this context I will also illustrate how various dynamical systems methods, such as, e.g., monotonic functions, center manifold techniques, averaging methods, can yield a global understanding of the solution spaces as well as approximations, complementing, e.g., the slow-roll approximation.