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The dark matter problem is one of the most pressing problems in modern physics. As there is no well-established claim from a direct detection experiment supporting the existence of the illusive dark matter that has been postulated to…
We investigate torsion-driven cosmological dynamics within the framework of Einstein-Cartan gravity using the De Donder-Weyl Hamiltonian formalism, where the tetrad and Lorentz connection act as independent variables and the Hamiltonian…
Weyl conformal geometry may play a role in early cosmology where effective theory at short distances becomes conformal. Weyl conformal geometry also has a built-in geometric Stueckelberg mechanism: it is broken spontaneously to Riemannian…
We revisit Weyl's metrication (geometrization) of electromagnetism. We show that by making Weyl's proposed geometric connection be pure imaginary, not only are we able to metricate electromagnetism, an underlying local conformal invariance…
We show that we can derive the asymptotic Einstein's equations that arises at order $1/r$ in asymptotically flat gravity purely from symmetry considerations. This is achieved by studying the transformation properties of functionals of the…
We discuss gauge theories of scale invariance beyond the Standard Model (SM) and Einstein gravity. A consequence of gauging this symmetry is that their underlying 4D geometry is non-metric ($\nabla_\mu g_{\alpha\beta}\not=0$). Examples of…
Just after Weyl's paper (Weyl in Gravitation und Elektrizit\"at, Sitzungsber. Preuss. Akad., Berlin, 1918) Einstein claimed that a gravity model written in a spacetime geometry with non-metricity suffers from a phenomenon, the so-called…
We consider the Weyl-Dirac theory within the framework of the weak field approximation and show that the resulting gravitational potential differs from that of Newtonian by a repulsive correction term increasing with distance. The scale of…
We start by presenting the general set of structure equations for the 1+3 threading spacetime decomposition in 4 spacetime dimensions, valid for any theory of gravitation based on a metric compatible affine connection. We then apply these…
The gravitational interaction, as described by the Einstein-Cartan theory, is shown to emerge as the by-product of the spontaneous symmetry breaking of a gauge symmetry in a pre-geometric four-dimensional spacetime. Starting from a…
Two classes of stationary axisymmetric solutions of Einstein's equations for isolated differentially rotating matter sources are presented. The asymptotic regime is extracted, with attention to quasilocal gravitational energy, shear and…
We propose 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 spacetime manifold. For the matter we choose appropriate…
We present a new formulation for the canonical approach to conformal (Weyl-squared) gravity and its extension by the Einstein-Hilbert term and a nonminimally coupled scalar field. For this purpose we use a unimodular decomposition of the…
The galactic black hole is a supermassive black hole located at the center of a galaxy surrounded by a dark matter halo. For the first time, we establish a generic, fully-relativistic formalism to calculate solutions of Einstein's gravity…
The hypothesis that gravitational self-binding energy may be the source for the vacuum energy term of cosmology is studied in a Newtonian Ansatz. For spherical spaces the attractive force of gravitation and the negative pressure of the…
A unitary gravitational action up to third order of curvature in which respects to the holographic $a-$theorem has been constructed in \cite{myers}. In particular, its third order term is just the Weyl-cubed term in four dimensions. In this…
In a recent Comment on the paper "Dark matter as a Weyl geometric effect", by Burikham et al., Phys. Rev. D 107, 064008 (2023), posted on arxiv. org as eprint arXiv:2306.11926, it was claimed that the exact solution found in the above…
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 weak field limit for a pointlike source of a $f(R) \propto R^{3/2}$-gravity model is studied. We aim to show the viability of such a model as a valid alternative to GR + dark matter at Galactic and local scales. Without considering dark…
A conservative extension of general relativity by integrable Weyl geometry is formulated, and a new class of cosmological models ({\em Weyl universes}) is introduced and studied. A short discussion of how these new models behave in the…