Homogeneous isotropic cosmological model of space-time with torsion in the Einstein-Cartan theory of gravitation

A systematic treatment is applied to the cosmological problem in the Einstein-Cartan theory of gravitation on the basis of the variational principle formulated previously for an ideal fluid in space with torsion. Exact solutions are obtained for homogeneous isotropic cosmological models with flat three-dimensional space filled with powdery matter and a fluid with an equation of state p=/3.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 24–28, March, 1977.The author thanks Professor D. D. Ivanenko and members of the seminar conducted by him for useful discussions.     

Interacting quantum fields in a nonsingular cosmological model

The density of massless vector bosons created in a conformally flat nonsingular cosmological model is calculated.     

The Oppenheimer-Snyder space-time with a cosmological constant

We investigate the Oppenheimer-Snyder space-time with a positive cosmological constant A. The interior of the dust sphere is described by the closed Friedmann-Robertson-Walker space-time while the exterior is the Schwarzschild-de Sitter space-time. Due to the cosmological constant A, when the gravitational massM _o of the dust sphere is very large, there is no collapsing solution with the de Sitter-like asymptotic region which expands exponentially in the expanding universe frame. This fact suggests that the very large initial inhomogeneity does not necessarily lead to the failure of the cosmic no hair conjecture.     

Renormalization of a quantum field theory model in a curved space-time with torsion

A quantum field theory model that contains interacting non-Abelian gauge fields, scalar fields, and spinor fields is considered in a curved space-time with torsion. The cone-loop counterterms are found. It is shown that the multiplicative renormalization condition requires a nonminimal coupling of the matter with the gravitational field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 94–100, August, 1985.     

Einstein four-manifolds with skew torsion

We develop a notion of Einstein manifolds with skew torsion on compact, orientable Riemannian manifolds of dimension four. We prove an analogue of the Hitchin–Thorpe inequality and study the case of equality. We use the link with self-duality to study the moduli space of 1-instantons on S⁴$S^4$ for a family of metrics defined by Bonneau.     

Basic properties of the Einstein equations with a Ricci-Scalar-Dependent cosmological term

Basic properties of the Einstein equations modified by a cosmological Λ-term dependent on the Ricci scalar R are considered. We show that in addition to a nonzero divergence of the energy-momentum tensor of the matter and the consequent cold matter mass nonconservation as the Universe expands, this model suggests a significant modification of the equations for the gravitational potential and particle acceleration in the Newtonian approximation. These circumstances allow the necessary criteria for possible functional dependences Λ(R) to be formulated. Nevertheless, by introducing a variable Λ-term, we can look at the problems of dark matter and dark energy anew. In particular, we show that the model in which the cosmological term depends linearly on the Ricci scalar (this corresponds to the approximation of a more complex dependence in the case of low matter densities) makes it possible to satisfactorily describe the rotation curves of galaxies without invoking the dark matter hypothesis and to construct a cosmological model with a variable vacuum energy density, in qualitative agreement with the present views of the early Universe.     

Acceleration-enlarged symmetries in nonrelativistic space-time with a cosmological constant

By considering the nonrelativistic limit of de Sitter geometry one obtains the nonrelativistic space-time with a cosmological constant and Newton–Hooke (NH) symmetries. We show that the NH symmetry algebra can be enlarged by the addition of the constant acceleration generators and endowed with central extensions (one in any dimension (D) and three in D=(2+1)). We present a classical Lagrangian and Hamiltonian framework for constructing models quasi-invariant under enlarged NH symmetries that depend on three parameters described by three nonvanishing central charges. The Hamiltonian dynamics then splits into external and internal sectors with new noncommutative structures of external and internal phase spaces. We show that in the limit of vanishing cosmological constant the system reduces to the one, which possesses acceleration-enlarged Galilean symmetries.     

Self-consistent solutions of the semiclassical Einstein equations with cosmological constant

The general solution to the semiclassical backreaction equation is found for conformally invariant free quantum fields in spatially flat homogeneous and isotropic spacetime with Cosmological constant and with no classical source when the ratio of the renormalisation parameters/=9/4. It contains a two-parameter family of bouncing solutions that avoid the singularity. There are several one-parameter families which do not have particle horizons. The stability of these solutions is investigated and it is found that they are stable when and have different signs. However, when both parameters have the same sign the set of stable solutions is restricted by the condition 0 < < 1/9. In both cases these solutions have a final de Sitter stage.     

The superfluid vacuum state,time-varying cosmological constant,and nonsingular cosmological models

Some cosmological consequences of the superfluid vacuum state developed previously by the authors are discussed, particularly with regard to the initial stages of the universe. The transition temperature of the hadronic superfluid (superfluid during the hadron era) is estimated to be 10 ¹³ K, which is the same as the Hagedorn temperature, giving a physical basis of the thermodynamic bootstrap model.     

The cosmological term in the Einstein theory

It is proved that it is necessary to introduce in Einstein's equations a cosmological term proportional to the square of the λ-field strength which is related to the Lorentz group representation class ρμ = 0.     

Localization of torsion vibrations in a discrete model of alkanes

A simple coarse-grained model of a crystal of normal paraffin (the united-atom model) is considered. By using an original semi-inverse method, it is shown that, alongside with known polymorphic transitions, the model under consideration assumes a dynamic transition, which manifests itself in the localization of vibration energy at a certain threshold value of excitation energy. The prediction of the conditions of this transition requires analytical determination of the spectrum of nonlinear normal modes with arbitrary amplitudes of vibrations because the instability of the mode with the lowest wavenumber is a necessary energy localization condition. The equations obtained make it possible to investigate the resonance interaction between the nonlinear normal modes near the low-frequency edge of the spectrum resulting in capture of the vibration energy by one of the parts of the chain. The conditions of localization of the vibration energy revealed determine the necessary initial data for computer modeling of the predicted dynamic transition in normal paraffins.     

Rotation and acceleration as parallel transport in a space-time with torsion

We demonstrate that two simple noninertial motions, namely, uniformly rotating and uniformly accelerated motions, can be described as parallel transports, in a space-time manifold with torsion, of the moving object's reference frame along its world line. On the basis of that, it is conjectured that the electromagnetic field tensor is really only the temporal part of the contortion tensor. The only disturbing feature is that the decrease of the electromagnetic/gravitational coupling ratio with velocity (by the factor ) does not appear in this approach.     

“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.     

On the kinematics of the torsion of space-time

On a macroscopic level we take general relativity as the appropriate theory of space-time and gravity. We will argue that, on a more microscopic level, in the Compton wavelength regime of elementary particles, there are good reasons for suspecting the presence of a torsion of space-time. A corresponding gaugetheoretical formalism related to the Poincaré group is reviewed, and the kinematical consequences of the presence of a torsion are worked out. In particular we discuss the operational meaning and the measurability of torsion. The dynamics of torsion is left for a forthcoming article.     

Compactification over coset spaces with torsion and vanishing cosmological constant

We consider the compactification of ten-dimensional Einstein-Yang-Mills theories over non-symmetric, six-dimensional homogeneous coset spaces with torsion. We examine the Einstein-Yang-Mills equations of motion requiring vanishing cosmological constant at ten and four dimensions and we present examples of compactictifying solutions. It appears that the introduction of more than one radii in the coset space, when possible, may be mandatory for the existence of compactifying solutions.     

Two-component neutrino field and spherical symmetry in a space-time with curvature and torsion

The incompatibility of the spherical symmetry of a space-time with the presence of a “classical” i.e. not-quantized, 2-component neutrino field is extended from the purely Riemannian to the Riemann-Cartan geometry, corresponding to a space-time with curvature and torsion.