International Journal of Modern Physics D

An attempt is made here to extend to the microscopic domain the scale invariant character of gravitation — which amounts to consider expansion as applying to any physical scale. Surprisingly, this hypothesis does not prevent the redshift from being obtained. It leads to strong restrictions concerning the choice between the presently available cosmological models and to new considerations about the notion of time. Moreover, there is no horizon problem and resorting to inflation is not necessary.

We suggest novel statistics for the CMB maps that are sensitive to non-Gaussian features. These statistics are natural generalizations of the geometrical and topological methods that have been already used in cosmology such as the cumulative distribution function and genus. We compute the distribution functions of the Partial Minkowski Functionals for the excursion set above or bellow a constant temperature threshold. Minkowski Functionals are additive and are translationally and rotationally invariant. Thus, they can be used for patchy and/or incomplete coverage. The technique is highly efficient computationally (it requires only O(N) operations, where N is the number of pixels per one threshold level). Further, the procedure makes it possible to split large data sets into smaller subsets. The full advantage of these statistics can be obtained only on very large data sets. We apply it to the 4-year DMR COBE data corrected for the Galaxy contamination as an illustration of the technique.

The reheating process for the inflationary scenario is investigated phenomenologically. The decay of the oscillating massive inflaton field into light bosons is modeled after an out of equilibrium mixture of interacting fluids within the framework of irreversible thermodynamics. Self-consistent, analytic results for the evolution of the main macroscopic magnitudes like temperature and particle number densities are obtained. The models for linear and quadratic decay rates are investigated in the quasiperfect regime. The linear model is shown to reheat very slowly while the quadratic one is shown to yield explosive particle and entropy production. The maximum reheating temperature is reached much faster and its magnitude is comparable with the inflaton mass.

A generalization of the asymptotic wormhole boundary condition for the case of spacetimes with a cosmological horizon is proposed. In particular, we consider de Sitter spacetime with small cosmological constant. The wave functions selected by this proposal are exponentially damped in WKB approximation when the scale factor is large but still much smaller than the horizon size. In addition, they only include outgoing gravitational modes in the region beyond the horizon. We argue that these wave functions represent quantum wormholes and compute the local effective interactions induced by them in low-energy field theory. These effective interactions differ from those for flat spacetime in terms that explicitly depend on the cosmological constant.

Beginning from an effective theory in eight dimensions, in Ref. 1, Macias, Camacho and Matos proposed an effective model for the electroweak part of the Standard Model of particles in curved spacetime. Using this model, we investigate the cosmological consequences of the electroweak interaction in the early universe. We use the approximation that, near the Planck epoch, the Yang–Mills fields behave like a perfect fluid. Then we recover the field equations of inflationary cosmology, with the Higgs field directly related to the inflaton. We present some qualitative discussion about this and analyze the behavior of isospin space using some known exact solutions.

We apply the scale factor duality transformations introduced in the context of the effective string theory to the anisotropic Bianchi-type models. We find dual models for all the Bianchi-types [except for types VIII and IX] and construct for each of them its explicit form starting from the exact original solution of the field equations. It is emphasized that the dual Bianchi class B models require the loss of the initial homogeneity symmetry of the dilatonic scalar field.

The spherically symmetric thin shells of the macroscopically stable quark-gluon matter are considered within the frameworks of the bag model and theory of discontinuities in general relativity. The equation of state for the two-dimensional matter is suggested, and its features are discussed. The exact equations of motion of such shells are obtained. Distinguishing the two cases, circumstellar and microscopical shells, we calculate the parameters of equilibrium configurations, including the conditions of decay (deconfinement).

A new framework is proposed for general dynamic wormholes, unifying them with black holes. Both are generically defined locally by outer trapping horizons, temporal for wormholes and spatial or null for black and white holes. Thus wormhole horizons are two-way traversible, while blackhole and whitehole horizons are only one-way traversible. It follows from the Einstein equation that the null energy condition is violated everywhere on a generic wormhole horizon. It is suggested that quantum inequalities constraining negative energy break down at such horizons. Wormhole dynamics can be developed as for blackhole dynamics, including a reversed second law and a first law involving a definition of wormhole surface gravity. Since the causal nature of a horizon can change, being spatial under positive energy and temporal under sufficient negative energy, blackholes and wormholes are interconvertible. In particular, if a wormhole's negative-energy source fails, it may collapse into a blackhole. Conversely, irradiating a blackhole horizon with negative energy could convert it into a wormhole horizon. This also suggests a possible final state of blackhole evaporation: a stationary wormhole. The new framework allows a fully dynamical description of the operation of a wormhole for practical transport, including the back-reaction of the transported matter on the wormhole. As an example of a matter model, a Klein–Gordon field with negative gravitational coupling is a source for a static wormhole of Morris and Thorne.

We consider the problem of numerical computation of the Kolmogorov complexity and the fractal dimension of the anisotropy spots of Cosmic Microwave Background (CMB) radiation. Namely, we describe an algorithm of estimation of the complexity of spots given by certain pixel configuration on a grid and represent the results of computations for a series of structures of different complexity. Thus, we demonstrate the calculability of such an abstract descriptor as the Kolmogorov complexity for CMB digitized maps. The correlation of complexity of the anisotropy spots with their fractal dimension is revealed as well. This technique can be especially important while analyzing the data of the forthcoming space experiments.

A recent paper by Lima and Mohazzab has been examined and it is found that their results, that the Einstein field equations are consistent only for a dust and a turning point in the dynamics of the evolution is possible, are erroneous. This is due to their ignorance of the fact that the field equations and the energy conservation equation are not independent.