International Journal of Modern Physics D

We present a new non-parametric deprojection algorithm, DOPING (Deprojection of Observed Photometry using an INverse Gambit), which is designed to extract the three-dimensional luminosity density distribution ρ, from the observed surface brightness profile of an astrophysical system such as a galaxy or a galaxy cluster, in a generalised geometry, while taking into account changes in the intrinsic shape of the system. The observable is the 2D surface brightness distribution of the system. While the deprojection schemes presented hitherto have always worked within the limits of an assumed intrinsic geometry, in DOPING, geometry and inclination can be provided as inputs. The ρ that is most likely to project to the observed brightness data is sought; the maximisation of the likelihood is performed with the Metropolis algorithm. Unless the likelihood function is maximised, ρ is tweaked in shape and amplitude, while maintaining positivity, but otherwise the luminosity distribution is allowed to be completely free-form. Tests and applications of the algorithm are discussed.

Perturbation theory within Newtonian approximation is presented for cosmological models with time-varying physical constants. Analytical solutions for perturbations dynamics are obtained for each Gurzadyan–Xue model with pressureless matter and radiation. It is found that perturbations grow during the entire expansion within GX models, including the curvature- and vacuum-dominated stage when they cease to grow in the standard cosmological model.

In the context of the Brans–Dicke scalar tensor theory of gravitation, the cosmological Friedmann equation which relates the expansion rate H of the universe to the various fractions of energy density is analyzed rigorously. It is shown that the Brans–Dicke scalar tensor theory of gravitation brings a negligible correction to the matter density component of the Friedmann equation. Besides, in addition to Ω_Λ and Ω_M in the standard Einstein cosmology, another density parameter, Ω_Δ, is expected by the theory inevitably. Some cosmological consequences of such nonfamiliar cases are examined as far as recent observational results are concerned. Theory implies that if Ω_Δ is found to be nonzero, data can favor this model and hence this theory turns out to be the most powerful candidate in place of the standard Einstein cosmological model with cosmological constant. Such a replacement will enable more accurate predictions for the rate of change of the Newtonian gravitational constant in the future.

In 4 + 1 gravity the assumption that the five-dimensional metric is independent of the fifth coordinate permits the extra dimension to be either spacelike or timelike. As a consequence of this, the time coordinate and the extra coordinate are interchangeable, which in turn allows the conception of different scenarios in 4D from a single solution in 5D. In this paper, we make a thorough investigation of all possible 4D scenarios, associated with this interchange, for the well-known Kramer–Gross–Perry–Davidson–Owen set of solutions. We show that there are three families of solutions with very distinct geometrical and physical properties. They correspond to different sets of values of the parameters which characterize the solutions in 5D. The solutions of physical interest are identified on the basis of physical requirements on the induced matter in 4D. We find that only one family satisfies these requirements; the other two violate the positivity of mass-energy density. The "physical" solutions possess a lightlike singularity which coincides with the horizon. The Schwarzschild black string solution as well as the zero moment dipole solution of Gross and Perry are obtained in different limits. These are analyzed in the context of Lake's geometrical approach. We demonstrate that the parameters of the solutions in 5D are not free, as previously considered. Instead, they are totally determined by measurements in 4D — namely, by the surface gravitational potential of the astrophysical phenomena, like the Sun or other stars, modeled in Kaluza–Klein theory. This is an important result which may help in observations for an experimental/observational test of the theory.

One of the simplest ways to extend 4D cosmological models is to add another spatial dimension to make them 5D. In particular, it has been shown that the simplest of such 5D models, i.e. one in which the right-hand side of the Einstein equation is empty, induces a 4D nonempty universe. Accordingly, the origin of matter in a real 4D universe might be mathematically attributed to the existence of one (fictitious) extra spatial dimension. Here we consider the case of an empty 5D universe possessing a cosmological constant Λ and obtain exact solutions for both positive and negative values of the Λ. It is seen that such a model can naturally reduce to a power law ΛCDM model for the real universe. Further, it can be seen that the arbitrary constants and functions appearing in this model are endowed with definite physical meanings.

The analysis of a general multibody physical system governed by Einstein's equations is quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties — many coupled degrees of freedom, dynamic instability — are associated with the presence of gravitational waves. We have developed a number of "waveless approximation theories" (WAT's) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory.

In cosmology it has become usual to introduce new entities as dark matter and dark energy in order to explain otherwise unexplained observational facts. Here, we propose a different approach treating space–time as a continuum endowed with properties similar to those of ordinary material continua, such as internal viscosity and strain distributions originated by defects in the texture. A Lagrangian modeled on the one valid for simple dissipative phenomena in fluids is built and used for empty space–time. The internal "viscosity" is shown to correspond to a four-vector field. The vector field is shown to be connected with the displacement vector field induced by a point defect in a four-dimensional continuum. Using the known symmetry of the universe, assuming the vector field to be divergenceless and solving the corresponding Euler–Lagrange equation, we directly obtain inflation and a phase of accelerated expansion of space–time. The only parameter in the theory is the "strength" of the defect. We show that it is possible to fix it in such a way as to also quantitatively reproduce the acceleration of the universe. We have finally verified that the addition of ordinary matter does not change the general behavior of the model and that the proper Newtonian limit exists.

A time-dependent phenomenological model of Λ, viz. , is selected to investigate the Λ-CDM cosmology. The time-dependent form of the equation-of-state parameter ω is derived and it has been possible to obtain the sought-for flip of sign of the deceleration parameter q. The present age of the Universe, calculated for some specific values of the parameters, agrees very well with the observational data.

After briefly reviewing the relativistic approach to positioning systems based on the introduction of the emission coordinates, we show how explicit maps can be obtained between the Cartesian coordinates and the emission coordinates, for a suitably chosen set of emitters, whose world lines are supposed to be known by the users. We consider Minkowski space–time and the space–time where a small inhomogeneity is introduced (i.e. a small a "gravitational" field), in 1 + 1 and 1 + 3 dimensions.

There are three experimentally observed effects in rotating superconductors that are so far unexplained. Some authors have tried to interpret such phenomena as possible new gravitational properties of coherent quantum systems. In particular, they suggest that the gravitomagnetic field of that kind of matter may be many orders of magnitude stronger than the one expected in the standard theory. Here I show that this interpretation would be in conflict with the common belief that neutron stars have neutrons in a superfluid state and protons in a superconductive one.

It is shown that small volume elements of a perfect esentropic fluid move along geodesic lines of a Riemannian space–time.

We investigate an evolutional scenario of the FRW universe with the Casimir energy scaling like (-)(1 + z)⁴. The Casimir effect is used to explain the vacuum energy differences (its value measured in astrophysics is very small compared to the value obtained from quantum-field-theory calculations). The dynamics of the FRW model is represented in terms of a two-dimensional dynamical system to show all evolutional paths of this model in the phase space for all admissible initial conditions. We find also an exact solution for nonflat evolutional paths of the Universe driven by the Casimir effect. The main difference between the FRW model with the Casimir force and the ΛCDM model is that their generic solutions are a set of evolutional paths with a bounce solution and an initial singularity, respectively. The evolutional scenario is tested by using the SNIa data, FRIIb radiogalaxies, baryon oscillation peak and CMB observation. We compare the power of explanation of the model considered and the ΛCDM model using the Bayesian information criterion and the Bayesian factor. Our investigation of the information criteria of model selection showed preference for the ΛCDM model over other models considered. However, the presence of the negative-like radiation term can remove a tension between the theoretical and the observed primordial ⁴He and D abundance.