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We propose a model describing Einstein gravity coupled to a scalar field with an exponential potential. We show that the weak-field limit of the model has static solutions given by a gravitational potential behaving for large distances as…

Weyl's conformal theory of gravity is an extension of Einstein's theory of general relativity which associates metrics with 1-forms . In the case of locally integrable (closed non-exact) 1-forms the spacetime manifolds are no more simply…

We show that a class of solutions of minimal supergravity in five dimensions is given by lifts of three--dimensional Einstein--Weyl structures of hyper-CR type. We characterise this class as most general near--horizon limits of…

Rotation curves of spiral galaxies are known with reasonable precision for a large number of galaxies with similar morphologies. The data implies that non-Keplerian fall--off is seen. This implies that (i) large amounts of dark matter must…

The description of gravity in the form of an embedding theory is based on the hypothesis that our space-time is a four-dimensional surface in a flat ten-dimensional space. The choice of standard Einstein-Hilbert action leads in this case to…

A simple modification to Einstein's theory of gravity in terms of a non-Riemannian connection is examined. A new tensor-variational approach yields field equations that possess a covariance similar to the gauge covariance of…

We review (non-supersymmetric) gauge theories of four-dimensional space-time symmetries and their quadratic action. The only true gauge theory of such a symmetry (with a physical gauge boson) that has an exact geometric interpretation,…

The flattening of spiral-galaxy rotation curves is unnatural in view of the expectations from Kepler's third law and a central mass. It is interesting, however, that the radius-independence velocity is what one expects in one less…

We show how Einstein-Cartan gravity can accommodate both global scale and local scale (Weyl) invariance. To this end, we construct a wide class of models with nonpropagaing torsion and a nonminimally coupled scalar field. In…

A mysterious dark matter is supposed to exist in the galactic halos. In this contrast, we discuss the possibility of explaining the flat rotational velocity curves in f(R) gravity by solving field equations numerically in vacuum and for…

We provide a gauge-invariant theory of gravitation in the context of Weyl Integrable Space-Times. After making a brief review of the theory's postulates, we carefully define the observers' proper-time and point out its relation with…

In view of the observed flat rotation curves of spiral galaxies and motivated by the simple fact that within newtonian gravity a stationary axisymmetric mass distribution or dark matter vortex of finite extent readily displays a somewhat…

A classical nonlocal generalization of Einstein's theory of gravitation has recently been developed via the introduction of a scalar causal "constitutive" kernel that must ultimately be determined from observational data. It turns out that…

We introduce an extension of the Standard Model and General Relativity built upon the principle of local conformal invariance, which represents a generalization of a previous work by Bars, Steinhardt and Turok. This is naturally realized by…

In this paper we revisit the motivation and construction of a unified theory of gravity and electromagnetism, following Weyl's insights regarding the appealing potential connection between the gauge invariance of electromagnetism and the…

Here we give a more detailed account of the part of the conference report that was devoted to reinterpreting the Einstein `unified models of gravity and electromagnetism' (1923) as the unified theory of dark energy (cosmological constant)…

We discuss the concepts of Weyl and Riemann frames in the context of metric theories of gravity and state the fact that they are completely equivalent as far as geodesic motion is concerned. We apply this result to conformally flat…

We construct a class of static, axially symmetric solutions representing razor-thin disks of matter in an Integrable Weyl-Dirac theory proposed in Found. Phys. 29, 1303 (1999). The main differences between these solutions and the…

We develop a novel approach to the dark matter halos in the context of 4 dimensional Einstein--scalar-Gauss-Bonnet gravity to reproduce the flat rotation curves of galaxies. Moreover, the Gauss-Bonnet coupling describes the interior…

We investigated the possibility of construction the homogeneous and isotropic cosmological solutions in Weyl geometry. We derived the self-consistency condition which ensures the conformal invariance of the complete set of equations of…