Conformally coupled scalar field solutions and the cosmological constant

Solutions are presented for a scalar field coupled conformally to Einstein gravity with a nonvanishing cosmological constant, in the case that the spacetime metric is spatially homogeneous and isotropic. Since the cosmological constant destroys the conformal invariance of the action, these solutions cannot be obtained by solving the flat space wave equation for the scalar field. It turns out that the metric is determined entirely by the cosmological constant, while the scalar field acquires an apparent mass squared which is proportional to the cosmological constant. It is conjectured that the cosmological constant in the universe at present may thus be disguised as the mass of some scalar field.     

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.     

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.     

Conformally invariant field theories in two dimensions and corresponding statistical mechanical models

Belavin, Zamlodochikov and Polyakov have recently proposed a class of conformally invariant field theories in two dimension with exactly determined rational critical indices. We establish a tentative identification of a subset of these theories in terms of the O(n) model and theq-state Potts model in 2-dimensions for appropriaten andq. The results of this work were reported in the conference on “Structural Similarities in Exactly Solved Models” at I.T.P. Santa Barbara, August 1984.     

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.     

Production of scalar particles in cosmological models

The mean number of particles produced in a space-time with the metric ds²=dt²–t² (dx²+dy²)–Kt²dz²(=1/t², 1) is calculated. It is shown that the produced particles are described by a Bose-Einstein distribution with a certain temperature.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 3–6, July, 1980.I thank D. M. Gitman and V. P. Frolov for discussing a number of questions touched upon in the paper.     

Conformally flat tilted Bianchi Type-V cosmological models in general relativity

We have investigated two conformally flat tilted Bianchi Type-V cosmological models in general relativity. To get a determinate solution, we have assumed a supplementary conditionA =B ⁿ between metric potentials wheren is a constant. The behaviour of the model forn = 2 is discussed in detail. Various physical and geometrical aspects of the models are also discussed.     

Conformally invariant equations of the quantum field theory

The equations invariant under the transformation of the conformal algebra are obtained using the Casimir operators. The connections among the components of the field are explicitly derived in the case of indecomposable representations of the conformal algebra which give rise to e.g. the Maxwell equations with currents. The free field equations are also incorporated in the conformally covariant scheme.     

Five-dimensional cosmological models with massless scalar fields

Simple cosmologies are constructed from solutions of the five-dimensional Einstein equations with a real massless non-self-interacting scalar field source. It is demonstrated that non-trivial cosmological models occur only if the metric of the homogeneous and isotropic three-space of the universe has non-positive constant curvature. For the case of flat three-space, it is further demonstrated that two classes of solutions result - one of which has a power-law type of expansion for three-space and contraction of the one-dimensional internal space, while the other class has an exponential expansion for three-space and exponential contraction of the internal space. The exponentially expanding solutions are the limiting case of the power-law expanding solutions. Hence, our model is consistent with a simple inflationary scenario.     

Anisotropic cosmological models and generalized scalar tensor theory

In this paper generalized scalar tensor theory has been considered in the background of anisotropic cosmological models, namely, axially symmetric Bianchi-I, Bianchi-III and Kortowski-Sachs space-time. For bulk viscous fluid, both exponential and power-law solutions have been studied and some assumptions among the physical parameters and solutions have been discussed.     

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.     

Ultralocal scalar field models

In this paper the quantum theory of ultralocal scalar fields is developed. Such fields are distinguished by the independent temporal development of the field at each spacial point. Although the classical theories fit into the canonical framework, this is not the case for the quantum theories (with the exception of the free field). Explicit operator constructions are given for the field and the Hamiltonian as well as several other operators, and the calculation of the truncated vacuum expectation values is reduced to an associated single degree of freedom calculation. It is shown that construction of the Hamiltonian from the field, as well as the transition from the interaction to the noninteracting theories entails various infinite renormalizations which are made explicit.     

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.     

Exact hypersurface-homogeneous scalar field models

A mechanism is presented for obtaining exact solutions of the Einstein equations for hypersurface-homogeneous scalar fields which unifies and generalizes recent results for inflaton fields in the spatially homogeneous case and for thick domain walls in the timelike-homogeneous case.     

Survey of cosmological models with gravitational,scalar and electromagnetic waves

This paper gives an overview and reviews some recent investigations of anisotropic and inhomogeneous models. A class of models, which admit an Abelian two-parameter group of isometries, is considered in detail. Within this class of models we present exact solutions of the Einstein field equations. These solutions describe inhomogeneous cosmological models containing gravitational, scalar and electromagnetic waves. The solutions are used to study the effect of the symmetry breaking in corresponding Bianchi models. The nonlinear dynamics of primordial inhomogeneities is considered. The global evolution of the inhomogeneous models considered is also investigated. Finally we discuss the validity of various assumptions, used in the earlier treatments of inhomogeneous models.     

Conformally invariant fractals and potential theory

The multifractal (MF) distribution of the electrostatic potential near any conformally invariant fractal boundary, like a critical O(N) loop or a Q-state Potts cluster, is solved in two dimensions. The dimension &fcirc;(straight theta) of the boundary set with local wedge angle straight theta is &fcirc;(straight theta) = pi / straight theta-25-c / 12 (pi-straight theta)(2) / straight theta(2pi-straight theta), with c the central charge of the model. As a corollary, the dimensions D(EP) of the external perimeter and D(H) of the hull of a Potts cluster obey the duality equation (D(EP)-1) (D(H)-1) = 1 / 4. A related covariant MF spectrum is obtained for self-avoiding walks anchored at cluster boundaries.