Steering the universe

We discuss the present status of the Cauchy problem for Einstein's classical field theory of gravity.     

Measuring the universe

When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distributions of the sizes of cities, earthquakes, forest fires, solar flares, moon craters and people's personal fortunes all appear to follow power laws. The origin of power-law behaviour has been a topic of debate in the scientific community for more than a century. Here we review some of the empirical evidence for the existence of power-law forms and the theories proposed to explain them.     

Magnetic tension and the geometry of the universe.

The vector nature of magnetic fields and the geometrical interpretation of gravity introduced by general relativity guarantee a special coupling between magnetism and spacetime curvature. This magnetogeometrical interaction effectively transfers the tension properties of the field into the spacetime fabric, triggering a variety of effects with profound implications. Given the ubiquity of magnetic fields in the universe, these effects could prove critical. We discuss the nature of the magnetic-field--curvature coupling and illustrate some of its potential implications for cosmology.     

Antimatter in the universe

The models leading to a high abundance of antimatter in the universe are discussed. Special attention is payed to the model of antimatter creation in the form of compact stellar-like objects. Such objects can contribute significantly to the cosmological dark matter. Observational signatures of antimatter in the Galaxy are discussed.     

Rotation of the universe

We study the problem of a possible rotation of the observable Universe (Metagalaxy) from the point of view of the general-relativistic theory of gravitation. We employ the concept of a hierarchical structure of reality, based on the existence of Eddington-Dirac large numbers. From the Einstein equations in their Landau-Raichaudhuri form we derive expressions for the angular momentum and angular velocity of the rotation of the Metagalaxy. These expressions give an coinciding in order of magnitude with the observed one. Using the formulas obtained, and using the hierarchy relation (large number relation), we obtain the Stanyukovich formula S N^3/2 which relates the number of nucleons in the Metagalaxy N and its angular momentum S. We show that the angular velocity may decrease in inverse proportionality to the scale factor, which may explain its small value at this time. We show that the source of rotation in cosmology can be space-time torsion, induced by the spin of fermionic matter.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 12–16, March, 1987.The authors are grateful to V. F. Panov for the discussion of this paper and valuable comments.     

Rotation of the universe

The rate of rotation of the universe at the present time and in an early epoch is considered within the framework of the general theory of relativity. An approximate nonsingular model of the early universe with rotating matter is proposed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 58–62, September, 1987.     

Models of the universe

In this paper a theory of models of the universe is proposed. We refer to such models ascosmological models, where a cosmological model is defined as an Einstein-inextendible Einstein spacetime. A cosmological model isabsolute if it is a Lorentz-inextendible Einstein spacetime,predictive if it is globally hyperbolic, andnon-predictive if it is nonglobally-hyperbolic. We discuss several features of these models in the study of cosmology. As an example, any compact Einstein spacetime is always a non-predictive absolute cosmological model, whereas a noncompact complete Einstein spacetime is an absolute cosmological model which may be either predictive or non-predictive. We discuss the important role played by maximal Einstein spacetimes. In particular, we examine the possible proper Lorentz-extensions of such spacetimes, and show that a spatially compact maximal Einstein spacetime is exclusively either a predictive cosmological model or a proper sub-spacetime of a non-predictive cosmological model. Provided that the Strong Cosmic Censorship conjecture is true, a generic spatially compact maximal Einstein spacetime must be a predictive cosmological model. It isconjectured that the Strong Cosmic Censorship conjecture isnot true, and converting a vice to a virtue it is argued that the failure of the Strong Cosmic Censorship conjecture would point to what may be general relativity's greatest prediction of all, namely,that general relativity predicts that general relativity cannot predict the entire history of the universe.     

The deflationary universe: An instability of the de Sitter universe

The relevance is discussed of the initial value structure of the cosmological problem for inflationary explanations of its present structure. Existing proofs of the cosmic “no hair” conjecture are found to make use of an unrealistic strong energy condition on the stress tensor of the matter fields not driving the inflation. It is shown by explicit example that the no hair conjecture fails even in isotropic cosmological models if the strong energy conditions is relaxed. A class of exact cosmological models are given which begin in a de Sitter state but subsequently deflate towards the flat Friedman model. Various implications of these examples are discussed.     

Neutrinoless universe

We consider the consequences for the relic neutrino abundance if extra neutrino interactions are allowed, e.g., the coupling of neutrinos to a light (compared to m(nu)) boson. For a wide range of couplings not excluded by other considerations, the relic neutrinos would annihilate to bosons at late times and thus make a negligible contribution to the matter density today. This mechanism evades the neutrino mass limits arising from large scale structure.     

Scalar field fluctuations in the expanding universe and the new inflationary universe scenario

The behaviour of the scalar fied fluctuations in the exponentially expanding universe and their role in the new inflationary universe scenario are investigated.     

Semi-holographic universe

By assuming that a dark component (dark energy) in the universe strictly obeys the holographic principle, that is, its entropy is one fourth of the apparent horizon, we find that the existence of the other dark component (dark matter) is compulsory, as a compensation of dark energy, based on the first law of thermodynamics. By using the method of dynamical system analysis, we find that there exists a stable dark energy-dark matter scaling solution at late time, which is helpful to solve the coincidence problem. For reasonable parameters, the deceleration parameter is well consistent with current observations.     

Eigenvibrations of the expanding universe

A theoretical interpretation of the observed periodicity of large-scale (128 Mpc) correlations of galaxies is proposed as due to eigenvibrations of the closed expanding universe. Eigensolutions of the equations of motion for a scalar field in an inflationary model allow one to compute the energy density, interpreted as matter density. Isotropic eigensolution give rise to a matter density distribution having a periodic structure centered at the north pole of the closed Robertson-Walker universe represented by S³/Z₂. It is able to reproduce well the striking periodicity of the observational data, in the galactic north-south directions. The dipole and quadrupole eigensolutions and the location of the co-moving observer in a point of S³/Z₂ different from the center of the vibrational structure would imply, in a theoretically well predictable way, a decrease of the observed periodicity in some other directions.Partially supported by the State Committee for Scientific Research, Grant No. 2-0206-91-01.     

Rotation of the early universe

The evolution of the rotational velocity for the early expanding universe is analyzed. The possibility of a Planck rotational velocity is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 37–40, December, 1985.     

The homogeneity of the universe

The observational and philosophical grounds for our belief in the spatial homogeneity of the universe, are reconsidered. On the one hand, spatial homogeneity cannot be directly verified observationally, and, on the other hand, it raises a series of philosophical problems that counter its attractiveness to a considerable degree. It is pointed out that there are several possible alternative approaches to the question of the homogeneity of the universe that may provide at least as attractive a philosophical basis as the current approach and that merit detailed investigation as possible alternative bases for our cosmological world view.This essay received the first award from the Gravity Research Foundation for the year 1979.-Ed.     

On evolution of the universe

We consider the model of evolution of the Universe where the Big Bang is regarded as an explosion of a photon superstar. The inflationary epoch is not necessary in the model. The model describes the fundamental phenomena observed: the Universe is expanding at an increasing rate, it is homogeneous and isotropic and contains no antimatter, and its metrics is almost flat.     

Fluctuations in the inflationary universe

In the usual treatment of the inflationary universe, it is assumed that the expectation value of some component of the Higgs field develops a non-zero symmetry breaking value Φ₀. However, in the models normally considered, the expectation value of Φ will be zero at all times because Φ and ?Φ are equally probable. To overcome this difficulty, we calculate the effective action as a function of 〈Φ²〉 rather than 〈Φ〉. This also solves the infra-red problem associated with a Coleman-Weinberg condition in de Sitter space. The expectation value of Φ² grows linearly with time at first and then as (t₂ ? t^?1). The irregularities in the resulting universe are smaller than those predicted by previous authors, though in the case of the standard SU(5) GUT they are still bigger than the limit set by the microwave background.     

The smoothness of the universe

We study the evolution of primordial fluctuations in the Big Bang in the context of grand unified theories of elementary particle interactions. We show that dissipation due to grand unified viscosity strongly damps rotational modes of all frequencies, compressional modes of all except very low frequencies, and radiative modes of high frequencies. The damping mainly occurs at temperatures > 10¹⁵GeV, and does not significantly increase the entropy. Compressional modes which originate at high temperatures and have very low frequencies persist down to much lower temperatures and could eventually evolve into galaxies.