Cosmological lore—and some heresies

Cosmology is based on a number of well-founded assumptions, which include Hubble's law and the cosmological principle. Most cosmologists and astronomers also tacitly accept a number of other assumptions and beliefs which constitute a sort of traditional cosmological lore. Among these are the notions that the universe is finite, that if it is not, then there must be an observational horizon which renders it finite for all practical purposes, that it is valid to employ the special relativistic Doppler formula to interpret large cosmological redshifts, and that the expansion of the universe is slowing down toward its ultimate reversal. It is argued that none of these notions is incontrovertible and that some of them involve serious inconsistencies. An alternative approach is proposed which assumes that the universe is expanding uniformly and that it constitutes a fundamental reference frame for light propagation as implied by the Robertson-Walker metric. This approach leads to a model of the universe which is possibly infinite but without a specific observational horizon, and which satisfies the requirements of relativity. It is shown that the proposed model is theoretically consistent and that recent astronomical evidence supports its assumptions and predictions; it therefore presents a serious challenge to commonly held views about the universe.     

Cosmological term in the general theory of relativity and localization of the de Sitter and Einstein groups

The theory of a gauge gravitational field with localization of the de Sitter group is formulated. Starting from the tetradic components of the de Sitter universe, a relationship is established between the Riemannian metric and the de Sitter gauge field. It is shown that the general theory of relativity with the cosmological term is the simplest variant of the de Sitter gauge theory of gravitation, which transforms in the limit of an infinite radius of curvature of the de Sitter universe into the Poincaré-invariant GTR without the cosmological term. A theory of a gauge gravitational field with localization of Einstein's group of motions of the uniform static universe (the Einstein group R × S0 (4)) is formulated in an analogous manner.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 8, pp. 86–90, August, 1984.     

Initial-value problems and singularities in general relativity

Linearized solution of Datta in a non-symmetric and isentropic motion of a perfect fluid is studied by dealing with a Cauchy problem in co-moving coordinates in the framework of general relativity. The problem of singularities is discussed from the standpoint of a local observer both for rotating and non-rotating fluids. It is shown that, whatever the distribution of matter, a singularity which occurred in the past in both the rotating and non-rotating parts of the universe must occur again later after some finite proper time, if the universe is closed. A modification is incorporated in Penrose’s theorem by explicitly exhibiting that the universe defined by Penrose can possess a Cauchy hypersurface.     

Un-renormalized classical electromagnetism

This paper follows in the tradition of direct-action versions of electromagnetism having the aim of avoiding a balance of infinities wherein a mechanical mass offsets an infinite electromagnetic mass so as to arrive at a finite observed value. However, the direct-action approach ultimately failed in that respect because its initial exclusion of self-action was later found to be untenable in the relativistic domain. Pursing the same end, this paper examines instead a version of electromagnetism wherein mechanical action is excluded and self-action is retained. It is shown that the resulting theory is effectively interacting due to the presence of infinite forces. A vehicle for the investigation is a pair of classical point charges in a positronium-like arrangement for which the orbits are found to be self-sustaining and naturally quantized.     

A spin polarized disc. II

We present a solution to the gravitational field equations which describes either a static disc in general relativity or a spin polarized rotating disc in a Riemann-Cartan spacetime. The disc has infinite radius and finite thickness. The energy and pressure are finite and positive within the disc and for some parameter choices, a radial fall off in the fluid parameters is possible. A comparison is made to axis-symmetric wall solutions.     

Elementary physical approach to Mach's principle and its observational basis

It is shown that Mach's principle and the general principle of relativity are logical consequences of a materialistic postulate and that general relativity implies the validity of Mach's principle for a static (or quasistatic) homogeneous and isotropic universe, spatially self-enclosed. The finite velocity of propagation of gravitational field does not imply a retardation of inertial forces due to the distant masses and therefore does not exclude the validity of Mach's principle. Similarly, the experimentally verified isotropy of inertia is compatible with this principle. The recent observational evidence of very high isotropy of the actual universe proves that the anti-Machian Gödel world model must be rejected as a nonphysical one. This suggests the possibility of a renaissance of Einstein's first cosmological model by considering-in the spirit of an older idea of Herbert Dingle-a superlargescale quasistatic universe consisting of an unknown number of statistically oscillating regions similar to our own, momentarily expanding, metagalaxy.     

Effective Lagrangian for general relativity in presence of a quantized scalar field

New correction terms induced by a quantized scalar field vacuum on the Lagrangian of general relativity are investigated in case of an Einstein universe.     

A non-covariant theory of gravitation,I

Homogeneous isotropic models of the universe, based on the general theory of relativity, lead to the existence of a preferred frame of reference, which is similar to the absolute space of, Newton, and a preferred time coordinate, which resembles the absolute time of Newton. These concepts seem to be in contradiction to the principle of covariance on which the general relativity theory is based. A theory of gravitation is therefore proposed which uses the world picture of general relativity but is not covariant. In the three crucial tests, the proposed theory gives the same results as the general relativity theory. However, in contrast to general relativity, the present theory predicts the emission of gravitational waves by spherically symmetric systems, and gravitational waves are found, in general, to have both transverse and longitudinal components.     

New developments in the theory of gravity interacting with quantized fields

Renormalization in the theory of a quantized scalar field interacting with the classical Einstein gravitational field is discussed. The scalar field obeys the generalization of the Klein-Gordon equation which is conformally invariant in the limit of vanishing mass. A generalized Kasner metric corresponding to an anisotropic expansion of the universe is considered. Results obtained in collaboration with S.A. Fulling and B.L. Hu are described, which show explicitly how the infinities appearing in the expectation value of the energy-momentum tensor can be absorbed through renormalization of the cosmological constant and the coefficients of a quadratic tensor appearing in a slightly generalized form of the Einstein equation. There is also a finite renormalization of the gravitational constant.     

Signal propagation in the general theory of relativity with viscosity and thermal conductivity: Linear theory

The Eckart-Landau-Lifshitz classical relativistic models of a viscous, heat-conducting fluid are known to lead to an infinite signal propagation velocity. This infinite value contradicts the postulate of a limiting signal velocity, equal to the velocity of light in vacuum. It is suggested that this paradox might be resolved by incorporating internal relaxation processes in the particles of the medium. It has been shown previously that in the special theory of relativity the velocity of a signal in a viscous, heat-conducting fluid with inheritance turns out to be finite. That assertion is proved in the present paper within the framework of the general theory of relativity in the approximation of a weak gravitational field.Institute of Earth Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 13–18, May, 1993.     

宇宙是无限和有限的统一

本文通过人类对宇宙认识的发展,阐明:1)宇宙在空间上是无限的,但无限不能脱离有限孤立存在。无限和有限是对立的统一,有限转化为无限,无限转化为有限。历史上形形色色的宇宙无限论和有限论,从牛顿的经典宇宙模型到现代宇宙学,都不能正确认识有限和无限的辩证法,结果都走上了形而上学和唯心论。2)宇宙在时间上也是无限的。宇宙万物不断发展,宇宙总体无始无终,宇宙不动论是错误的,人类对宇宙的认识发展深刻阐明:宇宙是绝对无限和相对有限的对立统一。     

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.     

Brief History of a Relativistic Century

More than one century is passed by the publication of special relativity and few less by the birth of general relativity. Despite the great experimental successes of these theories, the study of the universe, is plagued by numerous unsolved problems. For example one of the most problems in cosmology is the cosmological constant, which governs the expansion of the universe, also known as dark energy. A substantial portion, about 60%, of the mass-energy in the universe is in a form of mysterious energy that is pushing the cosmos apart at an accelerating rate. What is this energy, and where does it come from? Cosmologists have no real idea. Although given a similar name, there is another problem in cosmology, the so-called dark matter, which is actually unrelated to dark energy, except insofar as they involve things we don’t understand. About 90% of the mass in the universe is in an apparently invisible form of matter that we call dark matter. This dark matter can only be measured by the gravitational pull it has on objects around it, and all galaxies we observe contain large halos of it, often extending for hundreds of thousands of light years beyond the edge of luminous matter. Is this dark matter actual matter, such as weakly interacting massive particles, or perhaps it is just an observational artifact caused by an improper theory of gravity? Another mystery is why there is so much more matter than antimatter in the universe. According to physical theories, these forms of matter are essentially equivalent, but conventional matter is observed in much greater abundances than antimatter. In this paper we summarily introduce the principal alternative theories proposed during one century of relativity.     

Non-Violation of Energy Conditions in the Future Accelerated Universe Due to Quantum Effects

Here, an accelerated phantom model for the late universe is explored, which is free from future singularity. It is interesting to see that this model exhibits strong curvature for all time in future, unlike models with ‘big-rip singularity’ showing high curvature near singularity time only. So, quantum gravity effects grow dominant as time increases in late universe too. More importantly, it is demonstrated that quantum corrections to FRW equations lead to non-violation of ‘cosmic energy conditions’ of general relativity, which are violated for accelerating universe without these corrections.     

Classical and relativistic forces of inertia

It is shown that — in contrast to the classical physics and special relativity — the self-consistency of general relativity requires that the forces of inertia follow unambiguously from the field equations as inductive gravitational effects of the cosmic matter and that this requirement is perfectly satisfied, without supplementary hypotheses, for the Einstein universe, in full agreement with Mach's principle.     

De Broglie-Bohm Interpretation of Canonical Quantum Cosmology Implies Early Stages of the Universe Dominated by Radiation

The Einstein's general relativity is formulated in the Hamiltonian form for a spatially flat, isotropic and homogeneous universe. Subsequently, we perform the canonical quantization procedure to the Hamiltonian to obtain the Wheeler-DeWitt equation. Solving the Wheeler-DeWitt equation and employing the de Broglie-Bohm interpretation to the wave function of the universe, we obtain a new version of spatially flat Friedmann equation for the early universe where the scale factor of the universe is taken to be sufficiently small.     

Cosmological models and Non-denumerable singularities

A review of the standard cosmological models shows that the positive cosmological constant gives rise to exponential increase in spatial extension. Such an increase is contradictory if extended over infinite future time, since even in an infinite universe there can only be a denumerable infinity of finite spatial units. The argument against exponential expansion is among the processes forbidden by the steady-state postulate of MacMillan.     

A note on infinities in eternal inflation

In some well-known scenarios of open-universe eternal inflation, developed by Vilenkin and co-workers, a large number of universes nucleate and thermalize within the eternally inflating mega-universe. According to the proposal, each universe nucleates at a point, and therefore the boundary of the nucleated universe is a space-like surface nearly coincident with the future light cone emanating from the point of nucleation, all points of which have the same proper-time. This leads the authors to conclude that at the proper-time t  =  t _nuc at which any such nucleation occurs, an infinite open universe comes into existence. We point out that this is due entirely to the supposition of the nucleation occurring at a single point, which in light of quantum cosmology seems difficult to support. Even an infinitesimal space-like length at the moment of nucleation gives a rather different result—the boundary of the nucleating universe evolves in proper time and becomes infinite only in an infinite time. The alleged infinity is never attained at any finite time.     

Entropic accelerating universe

To accommodate the observed accelerated expansion of the universe, one popular idea is to invoke a driving term in the Friedmann–Lemaître equation of dark energy which must then comprise 70% of the present cosmological energy density. We propose an alternative interpretation which takes into account the entropy and temperature intrinsic to the horizon of the universe due to the information holographically stored there. Dark energy is thereby obviated and the acceleration is due to an entropic force naturally arising from the information storage on the horizon surface screen. We consider an additional quantitative approach inspired by surface terms in general relativity and show that this leads to the entropic accelerating universe.