Cosmology as a search for overall equilibrium

The steps followed by Einstein when he first wrote on cosmology from the point of view of the general theory of relativity are revised. It is argued that his insightful line of thought leading to the introduction of the cosmological constant in the equations of motion has only one weakness: the constancy of the cosmological term, or what is the same, its independence of the matter content of the universe. Eliminating this feature, a simple and reasonable modification of the cosmological equations of motion is proposed. The solutions of the new cosmological equations give rise to a cosmological model that tries to approach the Einstein static solution. This model exhibits very appealing features in terms of fitting current observations. The text was submitted by the author in English.     

Thermodynamics and cosmology

A new type of cosmological history which includes large-scale entropy production is proposed. These cosmologies are based on a reinterpretation of the matter-energy stress tensor in Einstein's equations. This modifies the usual adiabatic energy conservation laws, thereby leading to a possible irreversible matter creation. This creation corresponds to an irreversible energy flow from the gravitational field to the created matter constituents. This new point of view results from the consideration of thermodynamics of open systems in the framework of cosmology. It appears that the usual initial singularity is structurally unstable with respect to irreversible matter creation. The corresponding cosmological history therefore starts from an instability of the vacuum rather than from a singularity. The universe evolves through an inflationary phase. This appears to be an attractor independent of the initial vacuum fluctuation.This essay received the fifth award from the Gravity Research Foundation for the year 1988.-Ed.     

Cosmological Model Based on Gauge Theory of Gravity

A cosmological model based on gauge theory of gravity is proposed in this paper. Combining cosmological principle and field equation of gravitational gauge field, dynamical equations of the scale factor R(t) of our universe can be obtained. This set of equations has three different solutions. A prediction of the present model is that, if the energy density of the universe is not zero and the universe is expanding, the universe must be space-flat, the total energy density must be the critical density ρ_c of the universe. For space-flat case, this model gives the same solution as that of the Friedmann model. In other words, though they have different dynamics of gravitational interactions, general relativity and gauge theory of gravity give the same cosmological model.     

Limiting energy density and a regular accelerating universe in Riemann-Cartan spacetime

Isotropic cosmology built in the Riemann-Cartan spacetime by using sufficiently general expression of gravitational Lagrangian is investigated. It is shown that cosmological equations obtained by certain restrictions on indefinite parameters of gravitational Lagrangian lead to limiting energy density at the beginning of cosmological expansion and all cosmological models filled with usual gravitating matter satisfying standard energy conditions are regular with respect to energy density, spacetime metrics with its time derivative and torsion functions. At asymptotics cosmological solutions of spatially flat models coincide with that of standard ΛCDM-model for accelerating Universe.     

Thermodynamics and cosmology

A new type of cosmological history which includes large-scale entropy production is proposed. These cosmologies are based on a reinterpretation of the matterenergy stress tensor in Einstein's equations. This modifies the usual adiabatic energy conservation laws, thereby leading to a possible irreversible matter creation. This creation corresponds to an irreversible energy flow from the gravitational field to the created matter constituents. This new point of view results from the consideration of thermodynamics of open systems in the framework of cosmology. It appears that the usual initial singularity is structurally unstable with respect to irreversible matter creation. The corresponding cosmological history therefore starts from an instability of the vacuum rather than from a singularity. The universe evolves through an inflationary phase. This appears to be an attractor independent of the initial vacuum fluctuation.This work is reproduced in part from I. Prigogine, J. Geheniau, E. Gunzig, and P. Nardone (1989), Thermodynamics and Cosmology,General Relativity and Gravitation,21, 767.     

Emergent universe scenario via Quintom matter

The emergent universe scenario provides a possible alternative to bouncing cosmology to avoid the Big Bang singularity problem. In this Letter we study the realization of the emergent universe scenario by making use of Quintom matter with an equation of state across the cosmological constant boundary. We will show explicitly the analytic and numerical solutions of emergent universe in two Quintom models, which are a phenomenological fluid and a nonconventional spinor field, respectively.     

Georges Lemaître,Pioneer of Modern Theoretical Cosmology

No other scientist may have had a greater impact on modern cosmology than the Belgian physicist, astronomer and priest Georges Lemaître. In 1927 he predicted the expansion of the universe on the basis of the cosmological field equations; and four years later he proposed what he called the primeval-atom hypothesis, the first version of the later big bang universe. In all his work on cosmology the cosmological constant Λ played a significant role. A recognized expert in the theory of general relativity, Lemaître also contributed significantly to the theoretical clarification of local and global singularity problems. Still, when he died in 1968, at a time when the standard big bang model celebrated its first victories, he was largely forgotten or recalled only as a somewhat shadowy figure of the past. This essay reviews in a historical context the scientific work of Lemaître with particular attention to his seminal contributions in the decade between 1925 and 1934.     

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.     

“Bouncing” of simple cosmological models with torsion

The known cosmological solutions of the Einstein-Cartan-Sciama-Kibble (ECSK) field equations are reviewed. The prevention of singularities is explained by means of the extension of the Hawking-Penrose singularity theorems to the ECSK theory. Singularity prevention in semiclassical “spinning dust” models derives from the postulated form of the canonical energy-momentum and spin angular momentum tensors for the matter distribution. The effects of shear, vorticity, and pressure are examined. The singularity behavior of cosmological models incorporating the Dirac field as the source of the metric and torsion is discussed. In these models one finds an enhancement, rather than a prevention of singularity formation. Finally, the consequences of spin and torsion for observational cosmology and for particle creation in the early universe are noted.     

Exploring bouncing cosmologies with cosmological surveys

From recent observational data two significant directions have been made in the field of theoretical cosmology recently.First,we are now able to make use of present observations,such as the Planck and BICEP2 data,to examine theoretical predictions from the standard inflationaryΛCDM which were made decades of years ago.Second,we can search for new cosmological signatures as a way to explore physics beyond the standard cosmic paradigm.In particular,a subset of early universe models admit a nonsingular bouncing solution that attempts to address the issue of the big bang singularity.These models have achieved a series of considerable developments in recent years,in particular in their perturbative frameworks,which made brand-new predictions of cosmological signatures that could be visible in current and forthcoming observations.Herein we present two representative paradigms of early universe physics.The first is the reputed new matter(or matter-ekpyrotic)bounce scenario in which the universe starts with a matter-dominated contraction phase and transitions into an ekpyrotic phase.In the setting of this paradigm,we have proposed some possible mechanisms of generating a red tilt for primordial curvature perturbations and confront the general predictions with recent cosmological observations.The second is the matter-bounce inflation scenario which can be viewed as an extension of inflationary cosmology with a matter contraction before inflation.We present a class of possible model constructions and review the implications on the current CMB experiments.Lastly a review of significant achievements of these paradigms beyond the inflationaryΛCDM model is made,which is expected to shed new light on the future direction of observational cosmology.     

Relativistie Cosmology With Quantum Corrections

Homogeneous isotropic, anisotropic, and inhomogeneous cosmological models are studied using Einstein's general relativity with quntum corrections in field theoretical approximation. In particular we discuss coherent scalar fields and curvature squared terms in the gravitational Lagrangian. The conformal equivalence of the field equations of fourth order to general relativity with a scalar field as source is an example of the geometrization of a matter field. The aemiclassical quantum eorrections of the scalar fields can avoid the initial cosmological singularity and they lead to an inflationary evolution stage as transient attrator. The review provides new points of view on questions like the probability of the inflationary stage and the question of mechanisms for multiple inflation.     

Cosmological applications in Kaluza-Klein theory

The field equations of Kaluza–Klein (KK) theory have been applied in the domain of cosmology. These equations are solved for a flat universe by taking the gravitational and the cosmological constants as a function of time t. We use Taylor’s expansion of cosmological function, Λ(t), up to the first order of the time t. The cosmological parameters are calculated and some cosmological problems are discussed.     

Early Universe with Variable Gravitational and Cosmological Constants

Einstein field equations are considered in zero-curvature Robertson–Walker (R–W) cosmology with perfect fluid source and time-dependent gravitational and cosmological “constants.” Exact solutions of the field equations are obtained by using the ’gamma-law' equation of state p = (γ − 1)ρ in which γ varies continuously with cosmological time. The functional form of γ (R) is used to analyze a wide range of cosmological solutions at early universe for two phases in cosmic history: inflationary phase and Radiation-dominated phase. The corresponding physical interpretations of the cosmological solutions are also discussed.     

The creation of the universe as a quantum phenomenon

Quantum creation of massy particles can occur in the cosmological context without cost of energy. This fact is seized upon to construct a causal open homogeneous isotropic cosmology. The universe is conceived as the response of matter and the gravitational field to a spontaneous pointlike disturbance. Its history unfolds in two stages, creation and free expansion. The first stage gives rise to a “fireball.” The free expansion is extrapolated back to the “fireball.” The latter thus replaces the “big-bang,” thereby avoiding an initial singularity. Though not intrinsic to the theory it does suggest the interpretation of the cosmological part of the gravitational field as the scalar dilaton that is encountered in the dynamical generation of mass in conformally invariant theory.     

Gravitational perturbations in the expanding universe in a coordinate representation

Gravitational perturbations in the expanding universe are analyzed within the framework of Newtonian cosmology. In contrast to classical work, the perturbations are found not in a Fourier but in a coordinate representation. This makes it possible to obtain general expressions for finding the distributions of perturbations in the density and velocity of matter as a function of the coordinates and time from the known distribution at the initial time. In the simplest cases of plane-symmetric and spherically symmetric distributions, analytical equations are obtained for density perturbations as a function of the coordinates and time. The final conclusion is that it is possible for gravitational perturbations to grow even when the characteristic size of a perturbation is less than the Jeans wavelength. Kazan’ State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 45–52, March, 1997.     

Hořava–Lifshitz cosmology

The cosmological equations suggested by the non-relativistic renormalizable gravitational theory proposed by Hořava are considered. It is pointed out that the early universe cosmology has features that may give an alternative to inflation and the theory may be able to escape singularities.     

The confrontation of no-scale supergravity with cosmology

We present a number of exact cosmological solutions in the SU(1, 1)/U(1) “no-scale” theory of supergravity. We show that the auxiliary superfield acts as a negative stress and this permits the existence of a wide class of solutions which avoid the singularities that appear in the cosmological models of general relativity. However, by way of compensation, the dilation field always evolves so as to alter the sign of the coupling of matter to gravity in the vicinity of any expansion minimum or singularity. Moreover, the coupling of the dilation to any conventional matter sources present in the universe which is imposed by the theory does not appear to permit either power-law or exponential inflation to take place. The evolution of the mean expansion scale-factor is controlled by the auxiliary field density rather than by any conventional matter or inflaton fields present in the universe. These results indicate that classical “no-scale” supergravity theory (or at least its SU(1,1)/U(1) bosonic incarnation) may not provide acceptable models of the early universe.     

Cosmological applications in Kaluzaben Klein theory

The field equations of Kaluza-Klein (KK) theory have been applied in the domain of cosmology. These equations are solved for a flat universe by taking the gravitational and the cosmological constants as a function of time t. We use Taylor's expansion of cosmological function, Λ(t), up to the first order of the time t. The cosmological parameters are calculated and some cosmological problems are discussed.     

Cosmological Models with Time Dependent G and Λ Coupling Scalars

A cosmological model in which the universe has its critical density and gravitational constants generalized as coupling scalars in Einstein's theory is considered. A general method of solving the field equations is given. An exact solution for matter distribution in cosmological models satisfying G=G₀(R/R₀)ⁿ is presented. Corresponding physical interpretations of the cosmological solutions are also discussed.     

A model of the universe with decaying vacuum energy

The consequences of taking the total active gravitational mass of the universe phasewise constant together with a decaying vacuum energy in the background of Robertson-Walker space-time are investigated. The model so determined admits a contracted Ricci-collineation along the fluid flow vectorν ⁱ. It is geometrically closed but ever-expanding and does not possess the initial singularity, horizon, entropy, monopole or cosmological constant problems of the standard big bang cosmology. Estimates of the present matter; radiation and vacuum energy densities, the age of the universe and the present values of the deceleration parameter and the scale factor are also obtained.