Related papers: Paving the way for transitions --- a case for Weyl…
We use Weyl connection and Weyl geometry in order to construct novel modified gravitational theories. In the simplest case where one uses only the Weyl-connection Ricci scalar as a Lagrangian, the theory recovers general relativity.…
We consider Weyl gauge theories of gravity (WGTs), which are invariant both under local Poincar\'e transformations and local changes of scale. Such theories may be interpreted as gauge theories in Minkowski spacetime, but their…
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…
The notion of geometrical duality is discussed in the context of both Brans-Dicke theory and general relativity. It is shown that, in some particular solutions, the spacetime singularities that arise in usual Riemannian general relativity…
We consider a mimetic type extension of the Weyl geometric gravity theory, by assuming that the metric of the space-time manifold can be parameterized in terms of a scalar field, called the mimetic field. The action of the model is obtained…
In Part I of the present series of papers, we adumbrate our idea of Riemannian geometry to higher order in the infinitesimals and derive expressions for the appropriate generalizations of parallel transport and the Riemannian curvature…
We searched for a resolution of the flat galactic rotation curve problem from geometry instead of assuming the existence of dark matter. We observed that the scale independence of the rotational velocity in the outer region of galaxies…
We investigate the asymptotic symmetries of three-dimensional AdS Einstein gravity in the Weyl-Fefferman-Graham gauge, which is a generalization of the Fefferman-Graham gauge inducing a Weyl connection as part of the boundary structure. We…
We investigate the coupling of matter to geometry in conformal quadratic Weyl gravity, by assuming a coupling term of the form $L_m\tilde{R}^2$, where $L_m$ is the ordinary matter Lagrangian, and $\tilde{R}$ is the Weyl scalar. The coupling…
The Riemann tensor is the cornerstone of general relativity, but as everyone knows it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for…
We consider an $f(Q,T)$ type gravity model in which the scalar non-metricity $Q_{\alpha \mu \nu}$ of the space-time is expressed in its standard Weyl form, and it is fully determined by a vector field $w_{\mu}$. The field equations of the…
We consider the (gauged) Weyl gravity action, quadratic in the scalar curvature ($\tilde R$) and in the Weyl tensor ($\tilde C_{\mu\nu\rho\sigma}$) of the Weyl conformal geometry. In the absence of matter fields, this action has spontaneous…
Interesting phenomena and problems arising from the coupling of large-scale electromagnetic fields and spacetime curvature, are introduced and studied within this thesis. From electromagnetic wave propagation in curved spacetime to…
We consider an approach to Brans-Dicke theory of gravity in which the scalar field has a geometrical nature. By postulating the Palatini variation, we find out that the role played by the scalar field consists in turning the space-time…
We study various classical aspects of the Weyl transverse (WTDiff) gravity in a general space-time dimension. First of all, we clarify a classical equivalence among three kinds of gravitational theories, those are, the conformally-invariant…
We investigate the possibility that the observed behavior of test particles outside galaxies, which is usually explained by assuming the existence of dark matter, is the result of the dynamical evolution of particles in a Weyl type…
We investigate the cosmological evolution for the physical parameters in Weyl integrable gravity in a Friedmann--Lema\^{\i}tre--Robertson--Walker universe with zero spatially curvature. For the matter component, we assume that it is an…
We consider the construction of gauge theories of gravity, focussing in particular on the extension of local Poincar\'e invariance to include invariance under local changes of scale. We work exclusively in terms of finite transformations,…
During the last five decades, gravity, as one of the fundamental forces of nature, has been formulated as a gauge theory of the Weyl-Cartan-Yang-Mills type. The present text offers commentaries on the articles from the most prominent…
Already the simplest examples of Weyl geometry, the static space-time models of general relativity modified by an additional time-homogeneous Weylian length connection lead to beautiful cosmological models (Weyl universes) . The…