International Journal of Modern Physics A

Constraints on the Yukawa-type long-range interactions following from the Casimir effect are considered. The constraints obtained from the recent Casimir force measurements by means of a torsion pendulum and an atomic force microscope are collected and compared. New constraints are obtained from the measurement of the lateral Casimir force. The conclusion is made that the Casimir effect has an advantage over the conventional methods in obtaining stronger constraints on hypothetical interactions.

We compare metric theories to theories with teleparallelism and affine theories of gravity in order to discuss perspectives in the canonical quantization of gravity opened by a realization of Mach's principle.

The teleparallel equivalent of general relativity (TEGR) is an alternative formulation of Einstein's equations in the framework of Riemann-Cartan spacetimes. The gravitational field can be described either by the curvature of the torsion-free connection of general relativity (GR) or by the torsion of the curvature-free connection of the TEGR. Both in GR and TEGR the freedom in the choice of coordinates gives rise to the equivalence problem of deciding whether two solutions of the field equations are the same. This problem is solved by means of a invariant description of the gravitational field. We investigate whether the equivalence between GR and TEGR also holds at the level of these invariant descriptions. We show that the GR description assures equivalence in TEGR only in very special situations. These results are illustrated on teleparallel spacetimes with torsion and Gödel metric.

We discuss the isometry group structure of three-dimensional black holes and Chern–Simons invariants. Aspects of the holographic principle relevant to black hole geometry are analyzed.

The general dynamics of the spherically symmetric gravitational collapse of a massless scalar field is examined. We apply the Galerkin projection method to transform the partial differential equations ruling the dynamics of the collapse into a finite set of ordinary differential equations for the modal coefficients, after a convenient truncation procedure. We thus generate a dynamical system that not only reproduces the essential features of the dynamics of the gravitational collapse, even for a low order of truncation, but also discloses the structure of the dynamics. Each initial condition in modal space corresponds to a well defined spatial distribution of the scalar field. Numerical experiments with the system show that two main asymptotic configurations are possible: either the formation of a black hole or the dispersion of the scalar field leaving behind flat spacetime. Between the two asymptotic states there is a critical solution represented by a periodic orbit in the modal space with period Δ u ≈ 3.55. This periodic orbit acts as an intermediate attractor for the dynamics, being a limiting configuration for orbits generated from initial conditions in a critical surface of codimension one in the N-dimensional modal space. The compactness and fractality of this surface are briefly discussed.

The electromagnetic force a photon undergoes in a nonlinear regime can be geometrized. This is a rather unexpected result and at the same time a beautiful consequence of the analysis of the behavior of the discontinuities of non-homogeneous nonlinear electromagnetic field. We show how such geometrization is possible.

We study the massless Duffin-Kemmer-Petiau (DKP) equation in Riemannian space-times, particularly the massless spin 1 sector which reproduces the free Maxwell's equations.

The motivations for investigating a theory of gravitation based on a concept of "ether" are discussed — a crucial point is the existence of an alternative interpretation of special relativity, named the Lorentz-Poincaré ether theory. The basic equations of one such theory of gravity, based on just one scalar field, are presented. To check this theory in celestial mechanics, an "asymptotic" scheme of post-Newtonian (PN) approximation is summarized and its difference with the standard PN scheme is emphasized. The derivation of PN equations of motion for the mass centers, based on the asymptotic scheme, is outlined. They are implemented for the major bodies of the solar system and the prediction for Mercury is compared with an ephemeris based on general relativity.

The present paper is a polemic which describes how Inflation came on the scene and suggests a possible alternative.

We use a Riemannian four-dimensional presentation for gravitation in which the coordinates are distances and velocity rather than the traditional space and time. We solve the field equations and show that there are three possibilities for the Universe to expand. The theory describes the Universe as having a three-phase evolution with a decelerating expansion, followed by a constant and an accelerating expansion, and it predicts that the Universe is now in the latter phase. It is shown, assuming Ω_m = 0.245, that the time at which the Universe goes over from a decelerating to an accelerating expansion, occurs at 8.5 Gyr ago, at which time the cosmic radiation temperature was 146K. Recent observations show that the Universe's growth is accelerating. Our theory confirms these recent experimental results. The theory predicts also that now there is a positive pressure in the Universe. Although the theory has no cosmological constant, we extract from it its equivalence and show that Λ = 1.934 × 10^-35 s^-2. This value of Λ is in excellent agreement with measurements. It is also shown that the three-dimensional space of the Universe is Euclidean, as the Boomerang experiment shows.

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.

We summarize recent results concerning the evolution of second order perturbations in flat dust irrotational FLRW models with Λ ≠ 0. We show that asymptotically these perturbations tend to constants in time, in agreement with the cosmic no-hair conjecture. We solve numerically the second order scalar perturbation equation, and very briefly discuss its all time behaviour and some possible implications for the structure formation.

It is argued that the universe as a whole is not tractable as physical system. Since, as Mach stated, physical notions referring to the universe as a whole have no tangible sense because they imply applications of measurement notions to an object that is not accessible to measurement. Therefore, as well deductive cosmology as extrapolating cosmology contain fundamental difficulties.

The basic methods of searching for dark matter candidates are discussed. The main topics of this talk are: (a) ground - based cavity experiments with searching for galactic axions; (b) searching for hadronic axion decay line into galactic and extragalactic light; (c) experimental search for solar and stellar axions; (d) basic methods of searching for WIMPs as candidates into dark matter; (e) limits on axion and WIMP masses and their coupling constants to photons and ordinary matter; (f) novels of searching for nonbaryonic dark matter.

We reexamine the possibility of the detection of the cosmic topology in nearly flat hyperbolic Friedmann-Lemaître-Robertson-Walker (FLRW) universes by using patterns repetition. We update and extend our recent results in two important ways: by employing recent observational constraints on the cosmological density parameters as well as the recent mathematical results concerning small hyperbolic 3-manifolds. This produces new bounds with consequences for the detectability of the cosmic topology. In addition to obtaining new bounds, we also give a concrete example of the sensitive dependence of detectability of cosmic topology on the uncertainties in the observational values of the density parameters.

In the framework of inflationary models with non-vacuum initial states for cosmological perturbations, we study non-Gaussian signatures on the cosmic microwave background (CMB) radiation produced by a broken-scale-invariant model which incorporates a feature at a privileged scale in the primordial power spectrum.

We address three relevant questions related to the search for the size and shape of our Universe: (i) How do the actual observation of multiple images of certain cosmic objects, e.g. galaxy clusters, constrain the possible models for the shape of our Universe?, (ii) What kind of predictions can be done once a pair of cosmic objects have been identified to be topological images related by a translation?, and (iii) Is it possible to determine if two regions of space are topologically identified, even when distortions on the distributions of cosmic sources due to observational limitations are not negligible? We give examples answering the first two questions using the suggestion of Roukema and Edge that the clusters RXJ 1347.5-1145 and CL 09104+4109 might be topological images of the Coma cluster. For the third question, we suggest a method based on the analysis of PSH's noise correlations which seems to give a positive answer.

We briefly review the problem of embedding the spacetime in five dimensions and discuss the geometrical structure of a non-compactified version of Kaluza-Klein theory, known as induced-matter theory. We also highlight the importance of the embedding theorems of differential geometry in the context of embedding theories and present new results which may be considered as extensions of the Campbell-Magaard theorem.

We study the dynamical equations for extra-dimensional dependence of a warp factor and a bulk scalar in 5D brane world scenarios with 3+1 de Sitter slices. We show that these equations are similar to the equations for 4D scalar field cosmology, but with the sign of the scalar field potential reversed. We construct three dimensional phase portraits for this system for a variety of potentials. We show that for many potentials there will be an unavoidable singularity occuring a finite distance from the brane. This singularity can be shielded by the addition of a second brane. The properties of these branes will generally fix the inter-brane separation and effective 4D cosmological constants, thus providing a possible mechanism for stabilizing the braneworld. Some of these results were previously known for some models, but we bring together a variety of results and show how they can all be easily seen using phase portraits.

Corrections to Newtonian gravitation inspired by the extra dimensional physics and by the exchange of light and massless elementary particles between the atoms of two macrobodies are considered. These corrections can be described by the potentials of Yukawa-type and by the power-type potentials with different powers. The strongest up to date constraints on the corrections to Newtonian gravitation are collected following from the Eötvos- and Cavendish-type experiments and also from the measurements of the Casimir and van der Waals force.

It is shown that the coupling of the Kaluza-Klein (KK) internal scalar field both to an external stabilizing bulk scalar field and to the geomagnetic field may explain the observed dispersion in laboratory measurements of the (effective) gravitational constant. Except the PTB 95 value, the predictions are found in good agreement with all of the experimental data. The cosmological variation of the fine-structure constant is also addressed.

The problem of time-varying gravitational constant is discussed in frames of different theories of gravitation. Predictions for Ġ from multidimensional models and from generalized scalar-tensor theories are considered.

We discuss inflation in the Arkani-Hamed, Dimopoulos and Dvali scenario for extra dimensions. Basically we compare brane and bulk inflation. We restrict our discussion to chaotic and hybrid inflation models.

The modified Friedmann's equation is derived from the minimal set of postulates in the brane-world program. It is shown that the recently observed accelerated expansion of the universe can be explained in terms of the extrinsic curvature of the universe along the radial direction.

The nonplanar contribution to the effective action for massless scalar and vector fields on D– dimensional manifold with p compact noncommutative extra dimensions is calculated. The zeta function may not be regular at the origin. Thus, the related heat kernel trace has a logarithmic term in the short t asymptotic expansion. Consequences of this fact are briefly discussed.

The topological structure of Schwazschild's space-time and its maximal analytic extension are investigated in the context of brane worlds. Using the embedding coordinates, these geometries are seen as different states of the evolution of a single brane-world. Comparing the topologies and the embeddings it is shown that this evolution must be followed by a signature change in the bulk.

According to a recently proposed idea the indirectly observed negative pressure of our present universe might be explained by the trace anomaly of quantum chromo-dynamics (QCD) as a non-perturbative effect of quantum fields in curved space-times. Examining some of the consequences of the proposed mechanism for the cosmic evolution yields no apparent contradiction with our present picture of the universe. In conjunction with the weak anthropic principle a natural explanation of the cosmic coincidence can be provided. Further aspects such as the late-time behavior are also addressed.

We calculate the energy radiated by a uniformly moving charged scalar particle in the spacetime of a point-like global monopole, for small solid angle deficit. We show that this energy is proportional to the cube of the velocity of the particle and to the cube of the Lorenz factor, in the non-relativistic and ultra-relativistic cases, respectively. We also determine the energy shifts of a hydrogen atom placed in the background spacetime of a cosmic string and we discuss the possibility that these shifts could provide a means of probing for the presence of this topological defect in the Universe.

In this paper we consider a charged massless scalar quantum field operator in the spacetime of an idealized cosmic string which presents a magnetic field confined in a cylindrical tube of finite radius. Three distinct situations are taken into account in this analysis. In three cases the axis of the infinitely long tube of radius R coincides with the cosmic string. Because we study the combined gravitational and electromagnetic Aharanov-Bohm effect, we calculate the vacuum polarization effects outside the tube.

The original Casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. In this paper we develop the theory of a similar situation, involving a scalar field in spacetimes with closed spatial sections of negative curvature.

The quantization of the scalar and electromagnetic fields in the presence of a parabolic mirror is developed in the context of a geometric optics approximation. We calculate the mean squared scalar and electric fields near the focal line of a parabolic cylindrical mirror. These quantities are found to grow as inverse powers of the distance from the focus. We give a combination of analytic and numerical results for the mean squared fields. In particular, we find that the mean squared electric field can be either negative or positive, depending upon the choice of parameters. The case of a negative mean squared electric field corresponds to a repulsive Van der Waals force on an atom near the focus, and to a region of negative energy density. Similarly, a positive value corresponds to an attractive force and a possibility of atom trapping in the vicinity of the focus.

Quintessence tracking models have been put forward as a way of providing the missing cosmic energy required to make up for the shortfall between the observed clumped matter density and the critical density - as seems to be demanded by current observations - as well as simultaneously solving the initial condition problem faced by a cosmological constant. The robustness of this tracking quintessence scenario has recently been studied in more general cosmologies inspired by high-energy physics - cosmologies that include multiple scalar fields, brane corrections to the Hubble expansion law as well as potentials that decay with expansion. Here we give a summary of these results and apply them to the concrete case of a model with two scalar fields.

It is known that exponential particle creation can occur in situations which do not fall in the parametric resonance regime characterized by oscillations of the inflaton field about its minimum. Here we present a new analytical approach to exponential particle production which can occur when the inflaton is far from the minimum of its potential. Crucial for this effect is a term in the equation of motion which acts like a negative mass term, as occurs for tachyonic preheating and negative coupling particle production. Our techniques can be applied in models with a strong coupling between matter fields χ and the inflaton ϕ, or in some models in which the inflaton has a large amplitude of oscillation. On the other hand our analysis yields results which are quite model dependent. Although our analysis is general, in order to be clear we specialize, in this paper, to the model with interaction Lagrangian -g M_plϕχ².

We study a generally covariant model with SSB of scale invariance where two measures of integration in the action enter: the standard and a new Φd⁴x, where Φ is a density built out of degrees of freedom independent of the metric. The theory demonstrates a new mechanism for generation of the exponential potential: in the conformal Einstein frame, after SSB of scale invariance, the theory develops the exponential potential and, in general, non-linear kinetic term is generated as well. The scale symmetry does not allow the appearance of terms breaking the exponential shape of the potential that solves the problem of the flatness of the scalar field potential in the context of quintessential scenarios. Under normal laboratory conditions where the fermionic matter dominates, it is found that starting from a single fermionic field we obtain exactly three different types of spin 1/2 particles which can be identified with known fermion families. It is automatically achieved that for two of them, fermion masses are constants, the energy-momentum tensor is canonical and the "fifth force" is absent. For the third family, a self-interaction appears as a result of SSB of scale invariance.

N_T = 4 and N_T = 8 cohomological TQFT's in D = 2 are presented whose generators of topological shift, co–shift and gauge symmetry (Q^a, ^⋆Q^a, W) together with a discrete duality operation obey the same algebra as de Rham cohomology operators (d, δ, Δ) and the Hodge ⋆–operation.

The hypothesis that cold dark matter consists of primordial superheavy particles, the decay of short lifetime component of which led to the observable mass of matter while long living component survived up to modern times manifesting its presence in high energetic cosmic rays particles is investigated.

Numerical analysis of some regular inflationary cosmological models built in the framework of general relativity theory as well as gauge theories of gravitation is given. Dependence of some their characteristics on initial conditions at the bounce is discussed.

It is shown that cosmological models, based on the self-interacting scalar field theory or on the theory of the chiral non-linear sigma model. Can describe the global evolution of the Universe, extending from an inflationary stage to the present time epoch. The method of cosmological perturbations decomposition for inflaton and non-inflaton ones is applied for two-component chiral cosmological model in the spatially flat Friedmann-Robertson-Walker (FRW) Universe. New non-inflaton mode of cosmological perturbations is found.

In the light of recent observations which point to an open universe (Ω₀ < 1), we construct an open singularity-free cosmological model by reconsidering a model originally constructed for a closed universe. Our model starts from a nonsingular state called prematter, governed by an inflationary equation of state P = (γ_p - 1)ρ where γ_p (≃ 10^-3) is a small positive parameter representing the initial vacuum dominance of the universe. Unlike the closed models universe cannot be initially static hence, starts with an initial expansion rate represented by the initial value of the Hubble constant H(0). Therefore, our model is a two-parameter universe model (γ_p,H(0)). Comparing the predictions of this model for the present properties of the universe with the recent observational results, we argue that the model constructed in this work could be used as a realistic universe model.