Related papers: The Coupling of Shape Dynamics to Matter
Motivated by well-known obstacles to quantum gravity, I look for the most general geometrodynamical symmetries compatible with a reduced physical configuration space for metric gravity. I argue that they lead either to a completely static…
The 1+3 covariant approach and the covariant gauge-invariant approach to perturbations are used to analyze in depth conformal transformations in cosmology. Such techniques allow us to obtain very interesting insights on the physical content…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…
We examine "dynamical similarities" in the Lagrangian framework. These are symmetries of an intrinsically determined physical system under which observables remain unaffected, but the extraneous information is changed. We establish three…
A new approach to the dynamics of the universe based on work by O Murchadha, Foster, Anderson and the author is presented. The only kinematics presupposed is the spatial geometry needed to define configuration spaces in purely relational…
We consider first generation scalar-tensor theories of gravitation in a completely generic form, keeping the transformation functions of the local rescaling of the metric and the scalar field redefinition explicitly distinct from the…
We study a long-recognised but under-appreciated symmetry called "dynamical similarity" and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a…
We study gauge hierarchy problem of the Standard Model (SM) not by introducing new physics at the electroweak scale but by utilizing gravitational frames, frames generated by conformal transformations, as a renormalization medium. The…
We analyse the dynamical properties of disformally transformed theories of gravity. We show that disformal transformation typically introduces novel degrees of freedom, equivalent to the mimetic dark matter, which possesses a Weyl-invariant…
Starting from a topological gauge theory in two dimensions with symmetry groups $ISO(2,1)$, $SO(2,1)$ and $SO(1,2)$ we construct a model for gravity with non-trivial coupling to matter. We discuss the equations of motion which are connected…
We consider alternative theories of gravity with a direct coupling between matter and the Ricci scalar We study the relation between these theories and ordinary scalar-tensor gravity, or scalar-tensor theories which include non-standard…
It is shown that gravitation naturally emerges from the standard model of particle physics if local scale invariance is imposed in the context of a single conformal (Weyl-symmetric) theory. Gravitation is then conformally-related to the…
The possibility that global discrete dilation invariance is a fundamental symmetry principle of nature is explored. If the discrete self-similarity observed in nature is exact, then the Principle of General Covariance needs to be broadened…
We study conformal transformations in the most general parity-preserving models of the New General Relativity type. Then we apply them to analysis of cosmological perturbations in the (simplest) spatially flat cosmologies. Strong coupling…
We discuss the total collision singularities of the gravitational N-body problem on shape space. Shape space is the relational configuration space of the system obtained by quotienting ordinary configuration space with respect to the…
The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as…
Majorana's arbitrary spin theory is considered in a hyperbolic complex representation. The underlying differential equation is embedded into the gauge field theories of Sachs and Carmeli. In particular, the approach of Sachs can serve as a…
I present the first analytical study of gravitational collapse in a compact CMC foliation with $S^3$ spatial topology. The solutions I find, in this context, will be both solutions of Shape Dynamics and General Relativity. The aim is to…
We want to establish the basic properties of a scale invariant cosmology, that also accounts for the hypothesis of scale invariance of the empty space at large scales. We write the basic analytical properties of the scale invariant…
Isometrodynamics (ID), the gauge theory of the group of volume-preserving diffeomorphisms of an "inner" D-dimensional flat space, is tentatively interpreted as a fundamental theory of gravity. Dimensional analysis shows that the Planck…