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Inflation in the early universe can generate the nearly conformal invariant fluctuation that leads to the structures we observe at the present. The simple viable Starobinsky $R^2$ inflation has an approximate global scale symmetry. We study…
In this work we study the properties of rigidly rotating neutral dust solutions in general relativity. This class of solutions gained relevance recently due to applications to the dynamics of spiral galaxies. We show that this class could…
The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the…
To guarantee the stability of the cosmological constant sector against radiative corrections coming from quantum matter fields, one of the most natural ingredients to invoke is the symmetry under scale transformations of the gravitational…
We investigate the braneworld model with induced gravity to clarify the role of the cross-over length scale \ell in the possible explanation of the dark-matter phenomenon in astrophysics and in cosmology. Observations of the 21 cm line from…
This article analyzes the present anomalies of cosmology from the point of view of integrable Weyl geometry. It uses P.A.M. Dirac's proposal for a weak extension of general relativity, with some small adaptations. Simple models with…
Several approaches have been used to search for dark matter in our galactic disk, but with mixed results: {\em maybe yes and maybe no}. The prevailing approach, integrating the Poisson-Boltzmann equation for tracer stars, has led to more…
We investigate the equation of motion for photons with Weyl corrections in a Kerr black hole spacetime in a small coupling case. Our results show that Weyl corrections yield phenomena of birefringence. The light rays propagating in the…
The true nature of gravity is a remarkable open problem in Gravitation. Theoretical and observational motivations open the avenue of alternative theories of gravity. One possibility resorts to nonminimal couplings and non-metricity…
Here we follow the mainstream of thinking about physical equivalence of different representations of a theory, regarded as the consequence of invariance of the laws of physics -- represented by an action principle and the derived motion…
In the framework of Weyl-Dirac's theory a perturbed universe is considered. It contains luminous matter, dark matter consisting of weylons as well dark energy (DE) presented by Dirac's gauge function,\beta. A massive body creates a…
Some relations between conformal relativity and Weyl-Dirac theory are rephrased and clarified.
In this paper we obtain some cosmological solutions that describe the present period of accelerating expansion of the universe in the framework of a geometrical gauge scalar-tensor theory of gravity. The background geometry in the model is…
This note includes results of a study of stationary spherically symmetric ``dark holes'', objects merging central black holes and peripheral scalar graviton dark haloes arising in the framework of the modified gravity -- the quartet-metric,…
This paper has been withdrawn by the authors because the ratio presented in Eq. (13) does not remain frozen in time for all values of w = p/rho. As such a separate more detailed analysis containing the generalized Buchdahl inequality valid…
Shape dynamics is a classical theory of gravity which agrees with general relativity in many important cases, but possesses different gauge symmetries and constraints. Rather than spacetime diffeomorphism invariance, shape dynamics takes…
We consider a Weyl-Lorentz-$U(1)$-invariant gravity model written in terms of a scalar field, electromagnetic field and nonmetricity without torsion and curvature, the so-called symmetric teleparallel geometry, in three dimensions. Firstly,…
It is a well known fact that, in the absence of Dark Matter, the observation of the rotation curves of galaxies cannot be explained in terms of Newtonian gravity. Rotation curves become flat in the outer regions, in contrast to what is…
In this Letter we derive the gravity field equations by varying the action for an ultraviolet complete quantum gravity. Then we consider the case of a static source term and we determine an exact black hole solution. As a result we find a…
A novel oscillatory behaviour of the DC conductivity in Weyl semimetals with vacancies has recently been identified, occurring in the absence of external magnetic fields. Here, we argue that this effect has a geometric interpretation in…