International Journal of Modern Physics A

We have performed a precise experimental determination of the Casimir pressure between two gold-coated parallel plates by means of a micromachined oscillator. In contrast to all previous experiments on the Casimir effect, where a small relative error (varying from 1% to 15%) was achieved only at the shortest separation, our smallest experimental error (~ 0.5%) is achieved over a wide separation range from 170 nm to 300 nm at 95% confidence. We have formulated a rigorous metrological procedure for the comparison of experiment and theory without resorting to the previously used root-mean-square deviation, which has been criticized in the literature. This enables us to discriminate among different competing theories of the thermal Casimir force, and to resolve a thermodynamic puzzle arising from the application of Lifshitz theory to real metals. Our results lead to a more rigorous approach for obtaining constraints on hypothetical long-range interactions predicted by extra-dimensional physics and other extensions of the Standard Model. In particular, the constraints on non-Newtonian gravity are strengthened by up to a factor of 20 in a wide interaction range at 95% confidence.

Modern unification theories that seek to unify gravity with the other fundamental forces predict a host of new particles outside the standard model. Many also invoke extra dimensions. Both of these effects lead to deviations from Newtonian gravity. For sub micron distance between two bodies, the Casimir force far exceeds the gravitational force. Thus both understanding and using the Casimir force is very important for checking the relevance of these unification theories. In particular, measurements of the Casimir force has allowed one to set some of the strongest constraints for corresponding distance regions. This paper summarizes the techniques used to measure the Casimir force and some of the limits that follow from them.

We present an analysis, based on the center–edge asymmetry, to distinguish effects of extra dimensions within the Arkani-Hamed–Dimopoulos–Dvali (ADD) and Randall–Sundrum (RS) scenarios from other new physics effects in lepton-pair production at the CERN Large Hadron Collider LHC. Spin-2 and spin-1 exchange can be distinguished up to an ADD cutoff scale, M_H, of about 5 TeV, at the 95% CL. In the RS scenario, spin-2 resonances can be identified in most of the favored parameter space.

We review two recent developments on five-dimensional embedding theories of the spacetime: the embedding of branes, which is related to the Campbell-Magaard theorem, and the dynamics of particles in the context of the induced-matter theory. In the latter case, we show that there are two different ways of treating the anomalous acceleration of particles: the foliation and the embedding approach.

A large class of integrable cosmological models with two matter components is presented. The D-dimensional models on the space-time manifold are studied in the presence of 2 separately conserved barotropic perfect fluids. Such model are reducible to pseudo-Euclidean Toda-like system and integrable when their barotropic parameters satisfy some algebraic relations. Methods for integrating of pseudo-Euclidean Toda-like systems are based on the Minkowski-like geometry for characteristic vectors composed from the barotropic parameters. We also apply the methods for the spatially flat Friedmann-Robertson-Walker universe containing a perfect fluid and a minimally coupled self-interacting scalar field with a potential comprised of two exponentials.

We review some recent results concerning the properties of static, spherically symmetric configurations in RS2 type brane worlds: 1) Solving the trace of the effective 4D gravity equations, we obtain general classes of black hole and wormhole metrics, including families which unify symmetric wormholes, extremal black holes and non-extremal non-singular black holes. 2) Assuming (where is a part of the 5D Weyl tensor contributing to the 4D gravity equations), we show that material scalar fields confined on the brane may violate the no-hair theorem, support wormholes or form particlelike objects, but only at super-nuclear matter densities in the strong field region. 3) Solutions to the bulk field equations are found in case , among them solutions with a nonzero 4D cosmological constant, generalizing the so-called "black string".

We study a 6-dimensional Einstein-Born-Infeld-Higgs model. In the limit of infinite Born-Infeld coupling, this model reduces to an Einstein-Abelian-Higgs model, in which gravity localizing solutions were shown to exist. In this proceeding, we discuss further properties of the gravity localizing solutions as well as of the solutions in the limit of vanishing cosmological constant.

In the present article I give a five-dimensional interpretation of the Coulomb field in the context of Kaluza-Klein theory. It is shown that the projection into our four-dimensional world of the inertial dragging field due to a neutral particle moving around a closed fifth dimension, is interpreted as the electrical field of a charged particle from our four-dimensional point of view.

The confinement of classical and quantum test particles moving on a brane is studied by employing the notion of a returning force. It is shown that for classical test particles, the effects of extra dimensions are feeble whereas for quantum particles, these effects are pronounced. We also show that confinement causes the mass of a quantum particle to be quantized. Another consequence of the confinement is that it strongly restricts the choice of the bulk geometry even in the presence of the returning force.

We discuss the gravitomagnetism in the context of Brans-Dicke theory of gravity. We obtain the equation of motion of a particle in terms of gravitoelectric and gravitomagnetic fields. Comparing the result obtained with that predicted by general relativity we show that the difference between the two theories lies in the gravitomagnetic force.

Singularities in the metric of the classical solutions to the Einstein equations (Schwarzschild, Kerr, Reissner – Nordström and Kerr – Newman solutions) lead to appearance of generalized functions in the Einstein tensor that are not usually taken into consideration. The generalized functions can be of a more complex nature than the Dirac δ-function. To study them, a technique has been used based on a limiting solution sequence. The solutions are shown to satisfy the Einstein equations everywhere, if the energy-momentum tensor has a relevant singular addition of non-electromagnetic origin. When the addition is included, the total energy proves finite and equal to mc², while for the Kerr and Kerr–Newman solutions the angular momentum is mca. As the Reissner–Nordström and Kerr–Newman solutions correspond to the point charge in the classical electrodynamics, the result obtained allows us to view the point charge self-energy divergence problem in a new fashion.

Experimental tests of Newton law put stringent constraints on potential deviations from standard theory with ranges from the millimeter to the size of planetary orbits. Windows however remain open for short range deviations, below the millimeter, as well as long range ones, of the order of or larger than the size of the solar system. We discuss here the relation between long range tests of the Newton law and the anomaly recorded on Pioneer 10/11 probes.

Results from an almost twenty years study of radiometric data from Pioneer 10/11, Galileo and Ulysses spacecraft indicate an anomalous time depending blueshift^{1, 2} which bares hardly prosaic explanations. Local manifestation of the expansion of the universe or new force terms are not favored either by the observational data. So, we explore the possibility that the reported anomaly, referred to as the "Pioneer anomaly", does not result from a real change in velocity. It turns out that the main Pioneer anomaly may be looked at as a new validation of general relativity (GR) in the weak field and low velocity limit on account of the "machian" behavior of quintessence like dark energy.

The interaction between a charge and its electric field are analyzed in different situatuations. It is found that whether the charge is accelerated and its electric field lags behind, or in the case where the charge is static and its electric field falls in a gravitational field — in both cases the electric field curves, a stress force is created that acts as a reaction force, and radiation is created.

The existence of inhomogeneous and algebraically general silent universes with a positive cosmological constant is demonstrated and explicit solutions are given when one of the eigenvalues of the expansion tensor is 0.

In the article we review observational features of black holes where an influence of a gravitational field is dominant and we must use strong gravitational field approach for GR. Recent X-ray observations of microquasars and Seyfert galaxies reveal broad emission lines in their spectra, which can arise in the innermost parts of accretion disks. Simulations indicate that at low inclination angle the line is measured by a distant observer as characteristic two-peak profile. However, at high inclination angles (> 85°) two additional peaks arise. This phenomenon was discovered by Matt et al. (1993) using the Schwarzschild black hole metric to analyze such an effect. They assumed that the effect is applicable to a Kerr metric far beyond the range of parameters that they exploited. We check and confirm their hypothesis about such a structure of the spectral line shape for the Kerr metric case. We discuss how analysis of the iron spectral line shapes could give an information about an upper limit of magnetic field near black hole horizon.

In a SO(3,1)×U(1) framework, we analytically derive the first-order approximating solutions to the system of Klein–Gordon–Maxwell–Einstein equations describing a minimally coupled charged boson field to a spherically symmetric spacetime. Within a perturbative approach, we analyze the feedback of gravity and electric field on the charged scalar source and we get the coherent source-field regeneration rate. It turns out that we are dealing with an extremely short time-constant which is confirming the other authors' conclusion that intense gravitational bursts are accompanying the boson star formation.

We propose a generalization of gravitational interactions where the action contains, instead of the square root of the metric determinant, the square root of determinant of some other tensor field. We analyze the action as a possible alternative or addition to the Einstein gravity. Cosmological consequences of this hypothesis are briefly discussed.

Space time is described as a continuum four-dimensional medium similar to ordinary elastic continua. Exploiting the analogy internal stress states are considered. The internal "stress" is originated by the presence of defects. The defects are described according to the typical Volterra process. The case of a point defect in an otherwise isotropic four-dimensional medium is discussed showing that the resulting metric tensor corresponds to an expanding (or contracting) universe filled up with a non-zero energy-momentum density.

The parity and time reversal invariant actions, equations and their conjugated metric solutions are obtained in the context of a general relativistic model modified in order to suitably take into account discrete symmetries. The equations are not covariant however the predictions of the model, in particular its Schwarzschild metric solution in vacuum, only start to differ from those of General Relativity at the Post-Post-Newtonian order. No coordinate singularity (black hole) arises in the privileged coordinate system where the energy of gravity is found to vanish. Vacuum energies have no gravitational effects. A flat universe accelerated expansion phase is obtained without resorting to inflation nor a cosmological constant. The context may be promising to help us elucidate several outstanding enigmas such as the Pioneer anomalous blue-shift, flat galactic rotation curves or the universe voids.

We study oscillatory universes within the context of Loop Quantum Cosmology. We make a comparative study of flat and positively curved universes sourced by scalar fields with either positive or negative potentials. We investigate how oscillating universes can set the initial conditions for successful slow-roll inflation, while ensuring that the semi-classical bounds are satisfied. We observe rich oscillatory dynamics with negative potentials, although it is difficult to respect the semi-classical bounds in models of this type.

Models of gravity with variable G and Λ have acquired greater relevance after the recent evidence in favour of the Einstein theory being non-perturbatively renormalizable in the Weinberg sense. The present paper builds a modified Arnowitt–Deser–Misner (ADM) action functional for such models which leads to a power-law growth of the scale factor for pure gravity and for a massless ϕ⁴ theory in a Universe with Robertson–Walker symmetry, in agreement with the recently developed fixed-point cosmology. Interestingly, the renormalization-group flow at the fixed point is found to be compatible with a Lagrangian description of the running quantities G and Λ.

We treat the gravitational effects of quantum stress tensor fluctuations. An operational approach is adopted in which these fluctuations produce fluctuations in the focusing of a bundle of geodesics. This can be calculated explicitly using the Raychaudhuri equation as a Langevin equation. The physical manifestation of these fluctuations are angular blurring and luminosity fluctuations of the images of distant sources.

Non-singular global cosmic strings are found in a non-linear sigma model with a potential term for a self-gravitating complex scalar field. Stationary solutions with angular momentum and possibly linear momentum are obtained by assuming an oscillatory dependence of the scalar field on t, φ and z. This dependence has an effect similar to gauging the global U(1) symmetry of the model, which is actually a Kaluza-Klein reduction from four to three spacetime dimensions. The method of analysis can be regarded as an extension of the gravito-electromagnetism formalism beyond the weak field limit.

We investigate the vacuum expectation value of the energy-momentum tensor associated with a massive fermionic field obeying the MIT bag boundary condition on a spherical shell in the global monopole spacetime. The asymptotic behavior of the vacuum densities is investigated near the sphere center and surface, and at large distances from the sphere. In the limit of strong gravitational field corresponding to small values of the parameter describing the solid angle deficit in global monopole geometry, the sphere-induced expectation values are exponentially suppressed.

The rotation of astronomical objects may be of a cosmological origin due to the Universe's specific angular momentum estimates proving to exceed those for spiral galaxies. The problem is expected to be solved in the framework of quantum geometrodynamics.

We explicitly calculate the Green functions describing quantum changes of topology in Friedmann-Lemaître-Robertson-Walker Universes whose spacelike sections are compact but endowed with distinct topologies. The calculations are performed using the long wavelength approximation at second order in the gradient expansion. We argue that complex metrics are necessary in order to obtain a non-vanishing Green functions and interpret this fact as demonstrating that a quantum topology change can be viewed as a quantum tunneling effect. The result shows that the quantum topology changes in the direction of negatively curved hypersurfaces are strongly enhanced as time goes on, while transitions in the opposite direction are suppressed.

A semiclassical picture of black hole production in trans-Planckian collisions is reviewed.

Vacuum and dark energy energy problems are reviewed. Cosmology with non-zero vacuum energy is discussed. The astronomical data which indicate that the universe is filled with an anti-gravitating state of matter are described. The mechanisms which may lead to cancellation of almost infinite vacuum energy down to the astronomically observed value are enumerated with an emphasis to dynamical adjustment.

Recent high precision data by WMAP and SDSS have provided strong evidence to suggest that the universe is nearly flat. They are also making it possible to probe the topology of the universe. Motivated by these results, we have recently studied the consequences of taking the inflationary limit, i.e. |Ω₀ - 1| ≪ 0. We have shown that in this limit a generic detectable spherical or hyperbolic topology is locally indistinguishable from either or , irrespective of its global shape. Here we briefly present these results and further discuss their observational implications.

We present some consequences induced by nonlinear electrodynamics on the global properties of the universe.

We briefly review the physics of Big Bang Nucleosynthesis (BBN). We present, moreover, some recent results on active-sterile neutrino oscillations in the early universe and on their effects on BBN.

The possible resolution of the problem of cosmological singularity in the framework of gauge theories of gravitation is discussed. Generalized cosmological Friedmann equations for homogeneous isotropic models filled by scalar fields and usual gravitating matter and its solutions are investigated. Regular bouncing character of cosmological models is analyzed.

We demonstrate that the FRW model filled with dark energy fluid, satisfying the general form of the equation of state, p = w(z)ρ, can be reduced to the one-dimensional Hamiltonian flow. On the other hand we show that potential of this system can be reconstructed from the supernovae type Ia (SNIa) data. We show that the V-reconstruction method can be used to differentiate between dark energy models.

Assuming that higher dimensions existed in the early stages of the universe where the evolution was inflationary, we construct an open, singularity-free, spatially homogeneous and isotropic cosmological model to study the effects of dimensional reduction that may have taken place during the early stages of the universe. We consider dimensional reduction to take place in a stepwise manner and interpret each step as a phase transition. By imposing suitable boundary conditions we trace their effects on the present day parameters of the universe.

The cosmological (upper) limit on the Peccei-Quinn constant, related to the primordial oscillations of the axion field, can be relaxed for a mirror axion model. The simple reason is that the mirror world is colder and so the behavior of the axion temperature-dependent mass is dominated by the contribution from the mirror sector. So the coherent oscillations start earlier and correspondingly the axion mass density Ω_ah² is reduced.

It is widely believed that the large redshifts for distant supernovae are due to the vacuum energy dominance, which is responsible for the anti-gravitation effect. A tacit assumption is that particles move along geodesics for the background metric. This is in the same spirit as the consensus regarding the uniform Galilean motion of a free electron. However, apart from the Galilean solution, there is a self-accelerated solution to the Lorentz–Dirac equation governing the behavior of a radiating electron. Likewise, a runaway solution to the entire system of equations, both gravitation and matter equations of motion including, may exist, which provides an alternative explanation for the accelerated expansion of the Universe.

The physical space is believed to contain a kind of energy whose gravitational effect resembles the cosmological Λ-term introduced by Einstein. We discuss how the holographic conjecture, relating the universe entropy with the horizon area, may fix the late time variation of this effective Λ-term and the induced time dependence of the gravitational constant. The resulting cosmological solutions at late times present a constant ratio between the matter density and the vacuum energy density. It is then argued that, among the non-decelerating solutions, the coasting expansion is the only acceptable from a thermodynamic viewpoint. This solution is characterized by a universe age given by Ht = 1, and by density parameters Ω_m = 1/3 and Ω_Λ = 2/3, as required by the cosmic concordance model.

Connes' noncommutative approach to the standard model of electromagnetic, weak and strong forces is sketched as well as its unification with general relativity.

We show that the Einstein field equations for a Friedmann-Robertson-Walker(FRW) universe are completely equivalent to a generalized Ermakov-Milne-Pinney system. This extends recent work of R. Hawkins and J. Lidsey, and provides an alternate method for deriving exact solutions of the field equations.

We analyze the features of the near-horizon conformal symmetry of black holes from an algebraic point of view. The implications of such a symmetry for black hole entropy and decay are also discussed.

From Minkowskian 10D super Yang-Mills theory, by dimensional reduction and continuous Weyl-rotation, the 8D Euclidean, cohomological Spin(7)-invariant action is derived, by reduction to 7D the cohomological G₂-invariant action with global SU(2) symmetry obtains. Compatibility of chirality with generalized self-duality and octonionic algebra is shown. Using the chiral primary operator and the 8D analogue of the Pontryagin invariant a cohomological extension of has been constructed.

We show that most of the Bianchi A metrics with self-dual connection (hence self-dual Riemann curvature) have an integrable geodesic flow.

We show that the commonly known conductor boundary conditions E_‖ = B_⊥ = 0 can be realized in two ways which we call 'thick' and 'thin' conductor. The 'thick' conductor is the commonly known approach and includes a Neumann condition on the normal component E_⊥ of the electric field whereas for a 'thin' conductor E_⊥ remains without boundary condition. Both types describe different physics already on the classical level where a 'thin' conductor allows for an interaction between the normal components of currents on both sides. On quantum level different forces between a conductor and a single electron or a neutral atom result. For instance, the Casimir-Polder force for a 'thin' conductor is by about 13% smaller than for a 'thick' one.

The present work focuses on the scalar and electromagnetic fields in a spatially closed FRW Universe with incoherent dust. First, as the complex scalar field is under consideration, we derive the general solutions of the Gordon equation, in terms of the positive-frequency-like parity modes, and the corresponding propagator. Secondly, we turn to the source-free Maxwell equations in order to find a (1 + 4)-parametric class of closed form solutions representing a non-propagating fundamental electric field and a burst of electromagnetic radiation.

In the present work we show that planetary mean distances can be calculated through considering the Weyl geometry. We interpret the Weyl gauge field as a vector field associated with the hypercharge of the particles and apply the gauge concept of the Weyl geometry. The results obtained are shown to agree with the observed orbits of all the planets and of the asteroid belt in the solar system, with some empty states.