Related papers: A First-Principles Implementation of Scale Invaria…
H. Weyl's proposal of 1918 for generalizing Riemannian geometry by local scale gauge (later called {\em Weyl geometry}) was motivated by mathematical, philosophical and physical considerations. It was the starting point of his unified field…
We examine ways to write the Choptuik critical solution as the evolution of scale invariant variables. It is shown that a system of scale invariant variables proposed by one of the authors does not evolve periodically in the Choptuik…
We study first order equations of continuity and transport type on metric spaces of martingale dimension one, including finite metric graphs, p.c.f. self-similar sets and classical Sierpi\'nski carpets. On such spaces solutions of the…
The dynamical scaling of ageing ferromagnetic systems can be generalized to a local scale invariance. This yields a prediction for the causal two-time response function, which has been numerically confirmed in the Glauber-Ising model…
Scale invariant (transverse) gravitational theories are introduced. They are invariant under pure metric rescalings (i.e. the matter fields are inert under those). This symmetry forbids the presence of a cosmological constant. Those…
Cosmological perturbations of sufficiently long wavelength admit a fluid dynamic description. We consider modes with wavevectors below a scale $k_m$ for which the dynamics is only mildly non-linear. The leading effect of modes above that…
We discuss the initial-boundary value problem of General Relativity. Previous considerations for a toy model problem in electrodynamics motivate the introduction of a variational principle for the lapse with several attractive properties.…
General Relativity receives quantum corrections relevant at cosmological distance scales from the conformal scalar degrees of freedom required by the trace anomaly of the quantum stress tensor in curved space. In the theory including the…
We present a fully covariant and gauge-invariant analysis of linear cosmological perturbations in Energy-Momentum Squared Gravity. Working within the 1+3 formalism, we derive the exact propagation equations for scalar, vector, and tensor…
The effective theory of adiabatic fluctuations around arbitrary Friedmann-Robertson-Walker backgrounds - both expanding and contracting - allows for more than one way to obtain scale-invariant two-point correlations. However, as we show in…
A new class of gravity-matter models defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold are studied in some detail. These models involve…
The Scale Invariant Vacuum (SIV) theory rests on the basic hypothesis that the macroscopic empty space is scale invariant. This hypothesis is applied in the context of the Integrable Weyl Geometry, where it leads to considerable…
We propose a novel, higher-derivative, Weyl-invariant and generally-covariant theory for the cosmological constant. This theory is a mimetic construction with gauge fields playing the role of dynamical variables. These fields compose the…
A fundamental spacetime scale in the universe leads to noncommutative spacetime and thence to a modified energy - momentum dispersion relation or equivalently to a modification of Lorentz symmetry as shown by the author and others. This…
Barbour's interpretation of Mach's principle led him to postulate that gravity should be formulated as a dynamical theory of spatial conformal geometry, or in his terminology, "shapes." Recently, it was shown that the dynamics of General…
The symmetry reduction of dynamical systems that are invariant under changes of global scale is well-understood for classical theories of particles, and fields. The excision of the superfluous degree of freedom generating such rescalings…
We investigate the structure of the constraints on three-point correlation functions emerging when conformal invariance is imposed in momentum space and in arbitrary space-time dimensions, presenting a derivation of their solutions for…
Murray Gell-Mann, after co-inventing QCD, recognized the interplay of the scale anomaly, the renormalization group, and the origin of the strong scale, Lambda_{QCD}. I tell a story, then elaborate this concept, and for the sake of…
This paper invokes a new mechanism for reducing a coupled system of fields (including Einstein's equations without a cosmological constant) to equations that possess solutions exhibiting characteristics of immediate relevance to current…
An argument is made to show that the singularity in the General Theory of Relativity (GTR) is the expression of a non-Machian feature. It can be avoided with a scale-invariant dynamical theory, a property lacking in GTR. It is further…