The relationship betweenG andh in a closed Universe

In a closed expanding-contracting Universe, matter will be subject to an inward acceleration large enough to prevent perpetual expansion. A closed Universe must also perform a simple harmonic motion, which might consist either of one single cycle or of an infinite series of oscillations about a central point. It is the purpose of this study to find the rate ofa ₀, the cosmic acceleration, from which the gravitational constantG can be determined. It will be shown from Ampère's equation and Planck's radiation law that it is possible to derivea ₀=7.623×10^–12 ms^–2, a value which also conforms with the uncertainty principle. The relationship betweena ₀ and electromagnetic radiation is based on the concept that charges (such as electrons) must emit radiation while accelerating. The rate ofa ₀ yields a universal gravitational constant ofG=6.645×10^–11 N m² kg^–2.     

Is the Universe a white-hole?

Pathria (1972) has shown, for a pressureless closed Universe, that it is inside a black (or white) hole. We show now, that the Universe with a cosmic pressure obeying Einstein’s field equations, can be inside a white-hole. In the closed case, a positive cosmological constant does the job; for the flat and open cases, the condition we find is not verified for the very early Universe, but with the growth of the scale-factor, the condition will be certainly fulfilled for a positive cosmological constant, after some time. We associate the absolute temperature of the Universe, with the temperature of the corresponding white-hole.     

Black Hole in a Radiation-Dominated Universe

We study a black hole in an expanding Universe during the radiation-dominated stage. In particular, such a black hole may be of the primordial origin. In the case when the black hole radius is much smaller than the cosmological horizon, we found a self-consistent solution for the metric and the matter distribution and its velocity far from the black hole. At distances much smaller than the cosmological horizon our solution coincides with the previously obtained solution for quasi-stationary accretion. Our results can be applied, in particular, for the formation of dark matter density spikes around primordial black holes, and for the evolution of dark matter clumps during the radiation-dominated stage.     

Black Holes in a Violent Universe

“Black Holes in a Violent Universe” is a COST Action (MP0905) connecting scientists from different disciplines – astronomers from all wavelength regimes (i.e. radio to TeV), physicists and particle physicists, theoreticians and observers – from currently 25 countries. The aim is to collaborate in a cross-disciplinary and multi-dimensional approach towards a better understanding of the general Black Hole phenomenon. COST (European Cooperation in Science and Technology) is one of the longest-running European instruments supporting cooperation among scientists and researchers across Europe. The goal of MP0905 is to decipher further the way the Universe and the stars and galaxies evolved and – in particular – the role Black Holes play in this. This Action is an open and flexible program of communication and interchange.     

Global momentum loss in a non-expanding Universe

Applying the basic concepts of general relativity to the global motion of a particle in a mass-filled universe leads to a loss of momentum relative to the rest frame of the Universe. This loss is caused by the different running times of the gravitational interaction quanta exchanged with masses in front and behind the moving particle, if the signal velocity is limited to the speed of light. Due to this gravitational viscosity of space, the energy of photons will be reduced with the time, and thus with the distance of the emitting source. This red shift is superimposed on the Doppler shift in an expanding universe. A discussion of the limiting case of vanishing expansion leads to predictions about mass and radius of the Universe. The value of the mass density in such a steady-state universe must be about three times the closing density discussed in Big-Bang theories. The existence of the gravitational viscosity casts severe doubts on all estimations of the age of the Universe derived from the red-shift data.     

Density perturbations in a two-fluid component Universe

In a two-fluid component universe consisting of visible matter and neutrinos, the developed features of perturbations in the two components are quite different. If the densities ₁ and ₂, and the Jeans lengths _1J and _2J of the two components satisfy the relations ₁₂, _1J2J, the developed inhomogeneities in the non-dominant component 1 are larger than those in the dominant component 2. Moreover, the increase of perturbations is in some situations not monotonous but oscillatory, and such oscillations in the two components are contrary.     

The Evolution of Dilatonic Universe with a Double Exponential Potential

In this paper, dilaton in Weyl-Scaled induced gravitational theory is regarded as a candidate of dark energy. When the potential of dilaton field is taken as the form of a double exponential , we find that there exist attractor solutions in dilatonic dark energy model, and these attractors correspond to an equations of state and a cosmic density parameter , which are important features for a dark energy model that can meet the current observations. We find out the sufficient condition of the existence of a late time de Sitter attractor.     

On the Possibility of a Finite Model Describing the Universe

In his book “The expanding universe” EDDINGTON (1933) suggested the idea of an astronomical world model containing a finite number of material particles. Starting from this idea the author has speculated about the possibility to create a cosmological model where in addition also the number of geometrical points and time-instants is finite (JÄRNEFELT 1929, 1949, 1951, 1954a, 1954b, 1957, 1964, 1974, JÄRNEFELT and KUSTAANHEIMO 1952, JÄRNEFELT and QVIST 1955). The ultimate goal would be a world model based essentially upon GALOIS fields. In order to explore such a possibility the most simple actually existing physical system, the structure describing a non-relativistic free particle in an one-dimensional Euclidean space, is treated here. A discrete representation of this system is outlined and then a GALOIS -finitization of this platform is discussed. The author suggests that the method presented here for a very special case, could be generalizable and finally extended to a cosmological model.     

Reconstruction of the early Universe as a convex optimization problem

We show that the deterministic past history of the Universe can be uniquely reconstructed from knowledge of the present mass density field, the latter being inferred from the three-dimensional distribution of luminous matter, assumed to be tracing the distribution of dark matter up to a known bias. Reconstruction ceases to be unique below those scales – a few Mpc – where multistreaming becomes significant. Above 6 h ⁻¹ Mpc we propose and implement an effective Monge–Ampère–Kantorovich method of unique reconstruction. At such scales the Zel'dovich approximation is well satisfied and reconstruction becomes an instance of optimal mass transportation, a problem which goes back to Monge. After discretization into N point masses one obtains an assignment problem that can be handled by effective algorithms with not more than O ( N ³) time complexity and reasonable CPU time requirements. Testing against N -body cosmological simulations gives over 60 per cent of exactly reconstructed points.
We apply several interrelated tools from optimization theory that were not used in cosmological reconstruction before, such as the Monge–Ampère equation, its relation to the mass transportation problem, the Kantorovich duality and the auction algorithm for optimal assignment. A self-contained discussion of relevant notions and techniques is provided.     

The Value of Ωo in a Colliding Bubble Universe

We present a calculation of the probability distribution of the invariant separation between the nucleation centers of colliding bubbles resulting from the decay of a false de Sitter space vacuum. We also discuss the probability of a collision with a `third' bubble. This study is motivated by the proposed `colliding bubble braneworld' scenario in which the value of Ω₀ today is a function of this invariant. This revised version was published online in July 2006 with corrections to the Cover Date.     

Einstein–Rosen Universe in a Scalar-Tensor Theory of Gravitation

Field equations in the presence of a perfect fluid distribution are obtained in a scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. 113, 1985, 467) with the aid of Einstein–Rosen cylindrically symmetric metric. A static vacuum model and a non-static stiff fluid model are presented. The physical and geometrical properties of the stiff fluid model are studied.     

Physical uniformity of the Universe

The question of the spatial homogeneity of the Universe is re-examined from the viewpoint of the hypothesis on the physical unity of the universe. It is shown that the demand for the universal validity of the theory of relativity implies that the average value of the Newtonian world potential is constant everywhere in the universe which is spatially homogeneous on a large scale. It turns out that Mach's principle is compatible with the special theory of relativity if the average value of the normalized world potential is exactly equal to–c ². This fact may be interpreted as a consequence of the fundamental idea of the general relativity that cosmic matter determines the space-time metric in agreement with Mach's principle.     

Entropy of viscous Universe models

The cosmological event horizon entropy and the apparent horizon entropy of the ΛCDM and the Bianchi type I Universe model with viscosity has been calculated numerically, and analytically in the large time limit. It is shown that for these Universe models the cosmological event horizon entropy increases with time and for large times it approaches a finite maximum value. The effect of viscosity upon the entropy is also studied and we have found that its role is to decrease the entropy. The bigger the viscosity coefficient is the less the entropy will be. Furthermore, the radiation entropy for the ΛCDM Universe model with and without viscosity is investigated, and together with the cosmological event horizon entropy are used to examine the validity of the generalized second law of thermodynamics, which states that the total rate of change of entropy of the Universe is never negative, in this Universe model.     

Matter-space-time properties of the Universe

In the expansive nondecelerative homogeneous and isotropic relativistic Universe there take place: the permanent constant maximum possible creation of matter, the relativistic increase of mass of expanding objects, the relativistic dilatation of time of expanding objects, the relativistic contraction of radial length of expanding objects, and the relativistic dilatation of angular dimensions of expanding remote objects.Editor's Note: The delay in publishing this paper was due to an unfortunate oversight connected with the late Professor Kopal's death.     

General Relativistic Machian Universe

The Machian Universe, is usually described with Newtonian Physics, We give an alternative General Relativistic picture for Mach’s Universe. As such, we show that, in the correct Machian limit, Schwarzschild’s metric is coherent with Robertson-Walker’s, on condition that there be a cosmological constant, or the Universe’s rotation—or both. It is now confirmed that the Universe is accelerating, so the former condition applies. The latter was also confirmed one more time with the recently discovered NASA space probes anomalies. From Kerr-Lense-Thirring solution, we find an inverse scale-factor dependent angular speed; we then, show that the cosmological “constant” may have Classically originated from a centrifugal acceleration field.     

Five Dimensional Magnetic Universe

Possibility of a persistent structure of source free pure magnetic field contained by the curvature of a static cylindrically symmetric space-time associated with its own strength of energy density in five dimensional Kaluza-Klein space-time is investigated. It may be considered as the generalization of Melvin's 4D ‘magnetic universe’ in five dimensional K-K space-time. Time like and null geodesics are studied in order to investigate the nature of gravitation produced by it and are found not to deviate much from those noted in Melvin's spacetime. It is further interesting to note that near the axis of symmetry our 5D space-time exhibits the conical defect similar to that in the case of a string. This revised version was published online in July 2006 with corrections to the Cover Date.