Conformally invariant scalar field in charge-asymmetric cosmological models

Within a statistical approach to the general theory of relativity, we have constructed isotropic-charge-asymmetric cosmological models with an ultrarelativistic mixture of baryons and antibaryons and a conformally invariant scalar field. We have determined the role of the scalar field in the models obtained. We have investigated the evolution of small perturbations on the background of the spatially flat nonsingular model.Donets Polytechnical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 71–75, January, 1994.     

General relativity,the massless scalar field,and the cosmological constant

For gravity coupled to a neutral, massless scalar field, Wyman suggested a method of solution in power series valid provided the scalar field depends only on time. In this work we generalize his approach to nonzero cosmological constant.     

Exact solutions for the massless plane symmetric scalar field in general relativity,with cosmological constant

The Klein–Gordon equations are solved for the case of a plane-symmetric static massless scalar field in general relativity with cosmological constant, generalizing the solutions found by Taub, Novotny and Horsky, and Singh. A separate class of solutions is obtained in which the metrics reduce to flat space in the limit that .The static solutions can be used to generate time-dependent cosmological solutions, one of which exhibits rapid inflation followed by continued exponential expansion at all later times.     

On the Casimir energy for a massive quantum scalar field and the cosmological constant

We present a rigorous, regularization-independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass μ≠0 which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field in which the expectation value of the renormalized energy–momentum tensor is, for any fixed time, independent of the space coordinate and of the perfect fluid form g_μ,νρ with ρ>0, thus providing a concrete quantum field theoretic model of the cosmological constant. This ρ represents the energy density associated to a state consisting of the vacuum and a certain number of excitations of zero momentum, i.e., the constituents correspond to lowest energy and pressure p0.     

Inflation in cosmological models with a non-minimally coupled, massless scalar field

A homogeneous, spatially flat cosmological model induced by a massless scalar field is investigated. The parameter ξ of coupling of the field with the curvature can take any value. It is shown that the range of values of ξ is divided into three regions, ξ<0, 0<ξ<1/6, and ξ>1/6, each of which is characterized by the behavior of the scale factor in it. The points ξ=0 and ξ=1/6 are singular. Stages with exponential and power-law inflation are found in the ranges 0<ξ<1/6 and ξ>1/6. An exponential inflationary stage with acceptable cosmological consequences can occur for small positive ξ. Kazan’ State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 53–57, March, 1997.     

Type-D vacuum solutions with cosmological constant

All type-D vacuum (nonnull orbit and null orbit) solutions with are exhibited in canonical coordinates. The nonnull orbit metrics with contain four families of solutions: the static Levi-Cività metrics, the nondivergingD's, the divergingD's, and the diverging and twisting solutions. The null orbit metrics subdivide into two subclasses of solutions: the divergenceless null orbitD's, and the diverging and twisting null orbit solution.     

Nonsingular cosmological models: the massive scalar field case

The nonminimal coupling of a massive self-interacting scalar field with a gravitational field is studied. Spontaneous symmetry breaking occurs in the open universe even when the sign on the mass term is positive. In contrast to grand unified theories, symmetry breakdown is more important for the early universe and it is restored only in the limit of an infinite expansion. Symmetry breakdown is shown to occur in flat and closed universes when the mass term carries a wrong sign. The model has a naturally defined effective gravitational coupling coefficient which is rendered time-dependent due to the novel symmetry breakdown. It changes sign below a critical value of the cosmic scale factor indicating the onset of a repulsive field. The presence of the mass term severely alters the behaviour of ordinary matter and radiation in the early universe. The total energy density becomes negative in a certain domain. These features make possible a nonsingular cosmological model for an open universe. The model is also free from the horizon and the flatness problems.     

Radiating viscous universes coupled with zero-mass scalar field: Exact solutions

The dynamics of a radiating viscous fluid universe coupled with zero-mass scalar field is investigated in the Einstein formalism and two exact solutions are obtained. Both the solutions give expanding models. Their many physical and geometrical properties are studied. The model universe corresponding to the first solution turns out to be a big bang model. The second model shows an interesting feature of absorbing radiation rather than emitting it under certain conditions.     

Vacuum decay constraints on a cosmological scalar field

If the potential of a scalar field phi which currently provides the "dark energy" of the Universe has a minimum at phi = -M(0)(4)<0, then quantum-mechanical fluctuations could nucleate a bubble of phi at a negative value of the potential. This bubble would then expand at the speed of light. Given that no such bubble enveloped us in the past, we find that any minimum in V(phi) must be separated from the current phi value by more than min[1.5M(0),0.21M(Pl)], where M(Pl) is the Planck mass. We also show that vacuum decay renders a cyclic or ekpyrotic universe with M(0)(4) > or approximately 10(-10)M(4)(Pl) untenable.     

Higher-dimensional cosmological solutions with action of scalar and metric fields

An investigation is made of higher-dimensional (D5) cosmological solutions with action of scalar and metric fields for which a matter term is added. We restrict our attention to the most symmetric solutions with the structureM ^D–2×S ². We present the variant cosmological solutions for the symmetry breaking patternGSU(2)×U(1) (type IA, IIA) and patternGSO(3) (type IB, IIB). InD=6 case type IA is interesting for cosmology, which corresponds to a conformally invariant theory.     

Quantum cosmological model with a scalar field as source

It is shown that if both the conformal factor and scalar field are quantized on a background spacetime, a singularity-free cosmological model can be obtained and the quantum states must be zero-energy ones.     

A scalar field theory with a variable cosmological term

From the standpoint of cosmology, we investigate the relationship between the Brans-Dicke scalar field ø and the scalar field in particle physics (hereafter abbreviated as p.p.) on the assumption that ø is an arbitrary function ofr, but not oft. And also we see whether the cosmological term A which was originally introduced into cosmology without a relationship to p.p. can be related to the symmetry-breaking term in p.p., supposing a dependence of A upon ø.     

Inflationary stages in cosmological models with a scalar field

Homogeneous isotropic cosmological models with a massive scalar field are studied. It is shown that inflationary stages of evolution are characteristic of most solutions in these models.