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.     

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.     

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.     

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.     

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.     

General relativity as a conformally invariant scalar gauge field theory

The global symmetry implied by the fact that one can multiply all masses with a common constant is made into a local, gauge symmetry. The matter action then becomes Conformally invariant and it seems natural to choose for the corresponding scalar gauge field the action for a conformally invariant (massless) scalar field. The resulting conformally invariant theory turns out to be equivalent to general relativity. Since this means that the usual Einstein-Hilbert action is not, in fact, a true gauge action for the space-time geometry, the full theory ought to be supplied with such a term. Gauge-theoretic arguments and conformal invariance requirements dictate its form.     

Massive or massless scalar field and confinement

The generalization of QCD motivated classical SU(2) Yang-Mills theory coupled to a scalar field is discussed. The massive scalar field, corresponding to the scalar glueball, provides a confining potential for static, point-like, external sources. In the case of a massless scalar field screening solutions are found. However, there is a confining sector as well. Both, massive and massless confining solutions, are compared with phenomenological potentials. The case of a non-dynam ical permittivity is also discussed. Received: 15 November 2002 / Revised version: 31 January 2003 / Published online: 7 March 2003 RID="a" ID="a" e-mail: mslus@phys.ualberta.ca RID="b" ID="b" e-mail: wereszcz@alphas.if.uj.edu.pl     

Parameter estimation in n-dimensional massless scalar field

Quantum Fisher information(QFI) associated with local metrology has been used to parameter estimation in open quantum systems. In this work, we calculated the QFI for a moving Unruh–De Witt detector coupled with massless scalar fields in n-dimensional spacetime, and analyzed the behavior of QFI with various parameters, such as the dimension of spacetime, evolution time, and Unruh temperature. We discovered that the QFI of state parameter decreases monotonically from 1 to 0 over time. Additionall...     

Gravitational stability of a massless scalar field

A solution is obtained to the Einstein equations for a static, spherically symmetric, massless scalar field. The stability of a static, massless scalar field for a point source is studied. It is found that the field is unstable for small ratios of the scalar charge of the source to its mass but is stable for large ratios. It is proven that there exists a dimensionless number which limits the region of stability for the field.Translated from Izvestiya Vysshikh Uchebnyk Zavedenii, Fizika, No. 7, pp. 79–83.     

The cosmological constant and classical tests of general relativity

An upper limit of 10^-42 cm^-2 is placed on the absolute value of the cosmological constant by comparing with the prediction of the perihelion shift of Mercury. It is shown that the bending of starlight near the sun gives no limit on the cosmological constant since the equation for a null geodesic takes the same form with or without the cosmological constant.     

Two-dimensional quantum field theories containing a massless scalar field

The following new findings are briefly reported:

1. A consistent quantum theory can be formulated for a free massless scalar field in two-dimensional spacetime.
2. Satisfactory operator solutions in terms of asymptotic fields can be constructed in the Thirring and Schwinger models.
3. Gauge invariance is spontaneously broken in the Thirring model as well as in the Schwinger model.

     

On the free scalar massless field in two-dimensional space-time

In the present paper the solutions of the quantum field problem for the free scalar massless field in two-dimensional space time are constructed. It is shown that the fields obtained cannot vanish at space-like infinity. The latter fact implies the existence of two conserved charge operators. The transformation properties of these solutions under the two-dimensional Lorentz group are examined.     

Nonstatic solutions for the repulsive massless scalar field Einstein equation

Presented in this paper are exact nonstatic solutions for the coupled repulsive sourceless massless scalar field and the gravitational field. The solutions have the same form as the spatially conformally flat static metricds ² =e ^2ψ dt ² +e ^?2ψ(dx ² +dy ² +dz ²).     

Classical limit of the Casimir entropy for scalar massless field

We study the Casimir effect at finite temperature for a massless scalar field in the parallel plates geometry in N spatial dimensions, under various combinations of Dirichlet and Neumann boundary conditions on the plates. We show that in all these cases the entropy, in the limit where energy equipartitioning applies, is a geometrical factor whose sign determines the sign of the Casimir force.     

Free massless scalar field in two-dimensional space-time: Revisited

The indefinite-metric quantum field theory of the two-dimensional free massless scalar field proposed previously is reinvestigated. In order to reply to various criticisms of it, subtle points are discused in detail, and it is shown that the formalism is free from contradictions. In particular, its is emphasized that the non-uniqueness of the translationally invariant states is consistent with the irreducibility of the field algebra in the theory with indefinite metric.