Holographic considerations on a Machian Universe

MOND theory explains the rotation curves of the galaxies. Verlinde’s ideas establish an entropic origin for gravitational forces and Tsallis principle generalizes the theory of Boltzmann–Gibbs. In this work we have promoted a connection between these recent approaches, that at first sight seemed to have few or no points in common, using the Mach’s principle as the background. In this way we have used Tsallis formalism to calculate the main parameters of the Machian Universe including the Hubble parameter and the age of the Universe. After that, we have also obtained a new value for the Tsallis parameter via Mach’s principle. Using Verlinde’s entropic gravity we have obtained new forms for MOND’s well established ingredients. Finally, based on the relations between particles and bits obtained here, we have discussed the idea of bits entanglement in the holographic screen.     

Letter: Irreversible Processes in a Universe Modelled as a Mixture of a Chaplygin Gas and Radiation

The evolution of a Universe modelled as a mixture of a Chaplygin gas and radiation is determined by taking into account irreversible processes. This mixture could interpolate periods of a radiation dominated, a matter dominated and a cosmological constant dominated Universe. The results of a Universe modelled by this mixture are compared with the results of a mixture whose constituents are radiation and quintessence. Among other results it is shown that: (a) for both models there exists a period of a past deceleration with a present acceleration; (b) the slope of the acceleration of the Universe modelled as a mixture of a Chaplygin gas with radiation is more pronounced than that modelled as a mixture of quintessence and radiation; (c) the energy density of the Chaplygin gas tends to a constant value at earlier times than the energy density of quintessence does; (d) the energy density of radiation for both mixtures coincide and decay more rapidly than the energy densities of the Chaplygin gas and of quintessence.     

Causality in Inflationary Universes with Positive Spatial Curvature

We show that in the case of positively-curved Friedmann-Lemaître universes (k = +1), an inflationary period in the early universe will for most initial conditions not solve the horizon problem, no matter how long inflation lasts. It will only do so for cases where inflation starts in an almost static state, corresponding to an extremely high value of , 1, at the beginning of inflation. For smaller values, it is not possible to solve the horizon problem because the relevant integral asymptotes to a finite value (as happens also in the de Sitter universe in a k = +1 frame). Thus, for these cases, the causal problems associated with the near-isotropy of the Cosmic Background Radiation have to be solved already in the Planck era. Furthermore both compact space sections and event horizons will exist in these universes even if the present cosmological constant dies away in the far future, raising potential problems for M-theory as a theory of gravity.     

Nonsingularity in the no-boundary Universe

In the no-boundary Universe of Hartle and Hawking, the path integral for the quantum state of the Universe must be summed only over nonsingular histories. If the quantum corrections to the Hamilton-lacobi equation in the interpretation of the wave packet is taken into account, then all classical trajectories should be nonsingular. The quantum behaviour of the classical singularity in theS ¹×S ^m model (m⩾2) is also clarified. It is argued that the Universe should evolve from the zero momentum state, instead from a zero volume state, to a 3-geometry state.     

Letter: Density Perturbations in a Universe Dominated by the Chaplygin Gas

We study the fate of density perturbations in a Universe dominate by the Chaplygin gas, which exhibit negative pressure. In opposition to other models of perfect fluid with negative pressure, there is no instability in the small wavelength limit, due to the fact that the sound velocity for the Chaplygin gas is positive. We show that it is possible to obtain the value for the density contrast observed in large scale structure of the Universe by fixing a free parameter in the equation of state of this gas. The negative character of pressure must be significant only very recently.     

Photon Decays in the Radiation-Dominated Universe: Scalar Electrodynamics

The effect of the creation of an arbitrary number of massive pairs by a photon in the spatially flat model of the radiation-dominated Universe is considered. The process added-up probability is calculated within the framework of scalar quantum electrodynamics conformally related to the metric of a curved spacetime. The rate of photon decay in the radiation-dominated universe as well as the mean number of the created particles have been found. Comparison of the rate of the pair creation in the photon decays with the rate of the pair creation in the photon-photon collisions which take place in the Minkowski spacetime has been carried out. The estimates having been made show the number density of the particles created in the processes of the photon decays in the radiation-dominated Universe to be by a factor of 10³⁰ higher than the number density of the particles created from the vacuum of the free scalar field by the gravitational background.     

Dynamics of Extended Objects and a Stationary Axially Symmetric Cosmological Model

We find a new solution describing a homogeneous stationary axially symmetric model, which, in contrast to the Gödel model, does not contain closed timelike lines. We find exact solutions corresponding to the motion of a null string in the rotating Universe and show that these solutions crucially depend on the initial data. To obtain more detailed information on the cosmic string dynamics, we performed numerical simulations indicating essential differences in the behavior of strings and null strings in the presence of global rotation of the Universe. These numerical solutions show that the string manifests involved oscillations, varies its shape with the appearance of loops and cusps, and twists into a spiral.     

Energy-momentum localization in Marder space-time

Considering the Einstein, Møller, Bergmann-Thomson, Landau-Lifshitz (LL), Papapetrou, Qadir-Sharif and Weinberg’s definitions in general relativity, we find the momentum four-vector of the closed Universe based on Marder space-time. The momentum four-vector (due to matter plus field) is found to be zero. These results support the viewpoints of Banerjee-Sen, Xulu and Aydo?du-Salt?. Another point is that our study agrees with the previous works of Cooperstock-Israelit, Rosen, Johri et al.     

Singularity: Raychaudhuri equation once again

I first recount Raychaudhuri’s deep involvement with the singularity problem in general relativity. I then argue that precisely the same situation has arisen today in loop quantum cosmology as obtained when Raychaudhuri discovered his celebrated equation. We thus need a new analogue of the Raychaudhuri equation in quantum gravity.      

Why the Initial Infinite Singularity of the Universe Is Not There

We “explain”, using a Classical approach, how the Universe was created out of “nothing”, i.e., with no input of initial energy. This is a Universe with no-initial infinite singularity of energy density.