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,β. A massive body creates a spherically symmetric gravitational field, that is regarded as the perturbation of the homogeneous and isotropic universe [20]. Around the perturbing mass the dark energy forms up a ball-like concentration that reaches the horizon. The energy-mass density of this DE ball, the pressure and mass are searched. It turns out that they all are negative. As negative pressure is necessary to get acceleration at the expanding phase and deceleration during contraction, the Weyl-Dirac DE is an appropriate candidate. The negative mass of the DE ball is universally repulsive, both positive-mass and negative-mass objects will be pushed away by the ball. The negative DE mass and the negative DE pressure can be regarded as causing and supporting the present cosmic acceleration.

Some problems of cosmology: the big bang singularity, the origin of conventional matter, of dark matter and of dark energy may be successfully described and treated in the framework of the Weyl-Dirac theory. This theory, being a minimal expansion of Einstein's GRT, contains in addition to the metric tensor\g, the Weyl connection vector \w and the Dirac gauge function\beta. From these geometrically based quantities one obtains the behavior of our universe. The Weyl connection vector \w existing in microcells creates dark matter particles, weylons. In the very early universe \beta creates matter, whereas in the present dust period \beta forms dark energy, the latter causing cosmic acceleration. Around a massive body the - dark energy form a ball-like concentration having negative mass and negative pressure. These \beta-balls cause an additional acceleration of the expanding universe. The Weyl-Dirac theory is a classical geometrically based framework appropriate for describing and searching cosmology.

In the Weyl-Dirac (W-D) framework a spatially closed cosmological model is considered. It is assumed that the space-time of the universe has a chaotic Weylian microstructure but is described on a large scale by Riemannian geometry. Locally fields of the Weyl connection vector act as creators of massive bosons having spin 1. It is suggested that these bosons, called weylons, provide most of the dark matter in the universe. At the beginning the universe is a spherically symmetric geometric entity without matter. Primary matter is created by Dirac's gauge function very close to the beginning. In the early epoch, when the temperature of the universe achieves its maximum, chaotically oriented Weyl vector fields being localized in micro-cells create weylons. In the dust dominated period Dirac's gauge function is giving rise to dark energy, the latter causing the cosmic acceleration at present. This oscillatory universe has an initial radius identical to the Plank length = 1.616 exp (−33) cm, at present the cosmic scale factor is 3.21 exp (28) cm, while its maximum value is 8.54 exp (28) cm. All forms of matter are created by geometrically based functions of the W-D theory.

In the present work a procedure is build up, that allows obtaining dark matter (DM) and cosmic acceleration in our 4D universe embedded in a 5D manifold. Both, DM and the factor causing cosmic acceleration, as well ordinary matter are induced in the 4D space-time by a warped, but empty from matter, 5D bulk. The procedure is carried out in the framework of the Weyl–Dirac version (Israelit, Found Phys 35:1725, 2005; Israelit, Found Phys 35:1769, 2005) of Paul Wesson’s Induced Matter Theory (Wesson, Space-time matter, 1999) enriched by Rosen’s approach (Found Phys 12:213, 1982). Considering chaotically oriented Weyl vector fields, which exist in microscopic cells, we obtain cold dark matter (CDM) consisting of weylons, massive bosons having spin 1. Assuming homogeneity and isotropy at large scale we derive cosmological equations in which luminous matter, CDM and dark energy may be considered separately. Making in the given procedure use of present observational data one can develop a model of the Universe with conventional matter, DM and cosmic acceleration, induced by the 5D bulk.

Fundamental particles, regarded as the constituents of quarks and leptons, are described classicaly in the framework of the Weyl-Dirac version of Wesson's Induced Matter Theory. There are neutral particles and particles having charge Q=+/-(1/3e). The particles appear on the 4D brane, our universe, and are filled with a substance induced by the 5D bulk. This substace is taken to have mass density, charge density, pressure and is characterized by the prematter eq. of state P+ρ=0. The interior is separated from the surrounding vacuum by a boundary surface where the 4D metric tensor satisfies an a'la Schwarzschild condition. Outside of the boundary holds the Schwarzschild, or the Reissner-Nordstroem Metric, while the particles are characterized by mass, radius, charge.

A classical general relativistic theory possessing magnetic currents, as well electric ones and admitting massive photons was built up. As the geometric basis serves a space with Weylian non-metricity and torsion. The theory is coordinate covariant as well Weyl-gauge covariant. In the limit one obtains the ordinary Einstein-Maxwell theory.

Spherically symmetric entities filled with matter and induced by the 5D bulk may be built in the empty 4D space-time. The substance of the entity, the latter regarded as a fundamental particle, is characterized by the prematter equation of state P=−ρ. The particle is covered in a Schwarzschild-like envelope and from the outside it is characterized by mass and radius. One can regard these entities as neutral fundamental particles being constituents of quarks and leptons. The presented classical models are developed in the framework of a Weyl–Dirac version of Wesson’s Induced Matter Theory.

The foundations of Wesson’s induced matter theory are analyzed. It is shown that the empty—without matter—5-dimensional bulk must be regarded as a Weylian space rather than as a Riemannian one. Revising the geometry of the bulk, we have assumed that a Weylian connection vector and a gauge function exist in addition to the metric tensor. The framework of a Weyl–Dirac version of Wesson’s theory is elaborated and discussed. In the 4-dimensional hypersurface (brane), one obtains equations describing both fields, the gravitational and the electromagnetic. The result is a geometrically based unified theory of gravitation and electromagnetism with mass and current induced by the bulk. In special cases on obtains on the brane the equations of Einstein–Maxwell, or these of the original induced matter theory.

In Weyl’s geometry the nonintegrability problem and difficulties in defining measuring standards are reconsidered. Approaches removing the nonintegrability of length in the interior of atoms are given, so that atoms can serve as measuring standards. The Weyl space becomes a well founded framework for classical theories of electromagnetism and gravitation.

In the Integrable Weyl-Dirac theory we consider a spatially closed universe undergoing at present accelerated expansion, having a non-vanishing cosmological constant, and filled with luminous- and dark matter. During the dust-dominated period, dark matter and the quintessence pressure, the latter giving rise to acceleration: both are created by the Dirac gauge function. The behavior of F-R-W models is considered in appropriate gauges, and plausible scenarios are obtained. The outcome of the present paper, together with results of a previous work, provide a geometrically based, classical, singularity-free model of the universe. This has originated from a pure geometric Weyl-Dirac entity, passed a prematter period, the radiation-dominated era, and continues its development in the present dust period.

In the framework of an integrable Weyl–Dirac (W–D) theory a cosmological model is proposed. It describes a universe that began its expansion from a primary pre-Planckian geometric entity containing no matter. During the pre-Planckian period, from R 0 =5.58×10−36 cm to RI=5.58×10−34 cm, this embryonic universe has undergone a very rapid expansion and cosmic matter was created by geometry. At RI the universe was already filled with matter having the Planckian density ρ P and being in the state of prematter (P=−ρ), while the Weylian geometric elements were insignificant. This state is the Planckian egg that has served as the initial state of the singularity-free cosmological model (1) considered in the framework of Einstein's general theory of relativity. The W–D character of the geometry and the cosmological constant are significant in the pre-Planckian period during the matter creation. In the dust-dominated period a relic of the W–D geometry causes a global dark matter effect. In between the pre-Planckian and dust period one has Einstein's framework and Λ is negligible.

A spatially closed universe undergoing at present accelerated expansion, having a non-vanishing cosmological constant, and filled with luminous- and dark matter is described in terms of the Integrable Weyl–Dirac theory. It is shown that, during the dust-dominated period, dark matter and the quintessence pressure, the latter giving rise to acceleration: both are created by the Dirac gauge function. The behavior of two models: a nearly flat one and a well closed are considered in appropriate gauges, and plausible scenarios are obtained. The outcome of the present paper, together with results of a previous work,(31) provide a geometrically based, classical, singularity-free model of the universe, that has originated from a pure geometric Weyl–Dirac entity, passed a prematter period, the radiation-dominated era, and continues its development in the present dust period.

An integrable version of the Weyl-Dirac geometry is presented. This framework is a natural generalization of the Riemannian geometry, the latter being the basis of the classical general relativity theory. The integrable Weyl-Dirac theory is both coordinate covariant and gauge covariant (in the Weyl sense), and the field equations and conservation laws are derived from an action integral. In this framework matter creation by geometry is considered. It is found that a spatially confined, spherically symmetric formation made of pure geometric quantities is a massive entity. This may be treated either as a fundamental particle or as a cosmic body. In an F-R-W universe at the very beginning of the expansion phase the cosmic matter is created from an initial Planckian egg made of geometry, and during the following expansion geometric fields continue to stimulate the matter production.

This book shows that some unexplained cosmological and electrodynamic phenomena may be treated and understood in the geometrically based framework of Weyl and Dirac. After a short introductory chapter, Chapters 2 and 3 consider the Weyl-Dirac space-time as a geometric basis appropriate for building up relativistic theories. In the following chapter the Weyl-Dirac unified theory of gravitation and eletromagnetism, as well as its consequences, are discussed. Chapter 5 presents a modified version of the original Weyl-Dirac theory. In Chapter 6 the Weyl-Dirac theory enriched by Rosen's approach is considered as a source of geometrically based dark matter. Chapter 7 gives an integrable version of Weyl-Dirac theory, in which matter is created by geometry. In Chapter 8 an outlook of the Weyl-Dirac framework is given and its applicability to extended theories of electromagnetism, and cosmology is discussed.

Issuing from a geometry with nonmetricity and torsion we build up a generalized classical electrodynamics. This geometrically founded theory is coordinate covariant, as well as gauge covariant in the Weyl sense. Photons having arbitrary mass, intrinsic magnetic currents, (magnetic monopoles), and electric currents exist in this framework. The field equations, and the equations of motion of charged (either electrically or magnetically) particles are derived from an action principle. It is shown that the interaction between magnetic monopoles is transmitted by massive photons. On the other hand, the photon is massive only in the presence of magnetic currents. We obtained a static spherically symmetric solution, describing either the Reissner-Nordstrom metric of an electric monopole, or the metric and field of a magnetic monopole. The latter must be massive. In the absence of torsion and in the Einstein gauge one obtains the Einstein-Maxwell theory.

Including torsion in the geometric framework of the Weyl-Dirac theory we build up an action integral, and obtain from it a gauge covariant (in the Weyl sense) general relativistic massive electrodynamics. Photons having an arbitrary mass, electric, and magnetic currents (Dirac's monopole) coexist within this theory. Assuming that the space-time is torsionless, taking the photon mass zero, and turning to the Einstein gauge we obtain Maxwell's electrodynamics.

In a previous work the Weyl-Dirac framework was generalized in order to obtain a geometrically based general relativistic theory, possessing intrinsic electric and magnetic currents and admitting massive photons. Some physical phenomena in that framework are considered. It is shown that massive photons may exist only in the presence of an intrinsic magnetic field. The role of massive photons is essential in order to get an interaction between magnetic currents. A static spherically symmetric solution is obtained. It may lead either to the Reissner-Nordström metric, or to the metric created by a magnetic monopole.

On the basis of the Einstein equations, models of a spherically symmetric mass on a flat FRW background are investigated. Solutions are obtained with time-dependent homogeneous densities. These can be considered as describing either ordinary stars or exotic objects which become momentary black holes in the expanding universe.

A spherically symmetric entity with the Weyl-Dirac geometry holding in its interior is investigated. The structure is determined by the presence of the Dirac gauge function, which creates a mass density. Two models are obtained, one that can describe a cosmic body, the other an elementary particle.