On the induced cosmological term in quantum gravity

Tadpole diagrams where zero-momentum gravitons couple to massive matter loops lead to divergences which are not a consequence of infinite momentum integrals, but of the masslessness of the gravitons. It is shown that there exists no definition of these diagrams consistent with the Ward identities. They can be eliminated by an appropriate gauge choice, but then the BRS symmetry is spontaneously broken. Also in the scalar-tensor, conformally invariant formulation of quantum gravity, the tadpole problem does survive. The tadpole diagrams can, however, be cancelled by a cosmological counter-term. In that case, the Ward identities are satisfied.     

How to determine an effective potential for a variable cosmological term

It is shown that if a variable cosmological term in the present Universe is described by a scalar field with minimal coupling to gravity and with some phenomenological self-interaction potential V(ϕ), then this potential can be unambiguously determined from the following observational data: either from the behavior of density perturbations in dustlike matter component as a function of redshift (given the Hubble constant additionally), or from the luminosity distance as a function of redshift (given the present density of dustlike matter in terms of the critical value). Pis’ma Zh. éksp. Teor. Fiz. 68, No. 10, 721–726 (25 November 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

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.     

Gravitating Julia-Zee dyon and the cosmological term

The relation between the spherically symmetric Julia-Zee dyon of the coupled Yang-Mills-Higgs system and the cosmological term is studied in curved space-time. It is pointed out that the cosmological term comes out of the Higgs field.     

Evolution of the cosmological constant in effective gravity

In contrast to the phenomenon of nullification of the cosmological constant in equilibrium vacuum, which is the general property of any quantum vacuum, there are many options in modifying the Einstein equation to allow the cosmological constant to evolve in a nonequilibrium vacuum. An attempt is made to extend the Einstein equation in the direction suggested by the condensed matter analogy of the quantum vacuum. Different scenarios are found depending on the behavior of and the relation between the relaxation parameters involved, some of these scenarios having been discussed in the literature. One of them reproduces the scenario in which the effective cosmological constant emerges as a constant of integration. The second one describes the situation when, after the cosmological phase transition, the cosmological constant drops from zero to a negative value; this scenario describes the relaxation from this big negative value back to zero and then to a small positive value. In the third example, the relaxation time is not a constant but depends on matter; this scenario demonstrates that vacuum energy (or its fraction) can play the role of cold dark matter.     

Brans-Dicke cosmology with time-dependent cosmological term

Berman and Som's solution for a Brans-Dicke cosmology with time-dependent cosmological term, Robertson-Walker metric, perfect fluid, and perfect gas law of state solves the horizon, homogeneity, and isotropy problems without requiring any unnatural fine tuning in the very early universe, thus being an alternative model to inflation. The model also does not need recourse to quantum cosmology, and solves the flatness and magnetic monopole problems.     

Brans-Dicke models with time-dependent cosmological term

More general solutions than those presented by Bertolami are deduced in the Brans-Dicke cosmology, endowed with a time-dependent cosmological term, for a Robertson-Walker metric and a perfect fluid obeying the perfect gas law of state.     

A dynamical cosmological term from the Verlinde's maps

In this Letter it is proposed another generalization of the Verlinde's maps for the case Λ≠0$\Lambda \ne 0$. Thermodynamical arguments combined with this proposal conduce to a inverse square-law cosmological term behavior.     

The cosmological term,compensation and singularities

The necessity for the cosmological term in the Einstein and other theories of gravitation is emphasized; in these theories a “compensation” interpretation of the gravitational field as a calibration field is of fundamental importance and it leads, in particular, to torsion and nonlinearities for spinor and other fields. In conjunction with these ideas, the importance of allowing for exposed singularities is pointed out and their analogy with the latest elementary particle models is stressed.     

Homogeneous anisotropic solutions of einstein's equations with the cosmological term

Homogeneous anisotropic models of the Universe with a flat associated space full of pulverized material are derived, due allowance being made for the effect of the A term. It is shown that the presence of this term-whether positive or negative-accelerates the isotropization of the solution.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 117–120, December, 1971.     

The cosmological term and a modified Brans-Dicke cosmology

Adding the cosmological term , which is assumed to be variable in this paper, to the Brans-Dicke Lagrangian, we try to understand the meaning of the term and to relate it to the mass of the universe. We also touch upon the Dirac large-number hypothesis, applying the results obtained from the application of our theory to a uniform cosmological model.     

A cosmological concordance model with dynamical vacuum term

We demonstrate that creation of dark-matter particles at a constant rate implies the existence of a cosmological term that decays linearly with the Hubble rate. We discuss the cosmological model that arises in this context and test it against observations of the first acoustic peak in the cosmic microwave background (CMB) anisotropy spectrum, the Hubble diagram for supernovas of type Ia (SNIa), the distance scale of baryonic acoustic oscillations (BAO) and the distribution of large scale structures (LSS). We show that a good concordance is obtained, albeit with a higher value of the present matter abundance than in the ΛCDM model. We also comment on general features of the CMB anisotropy spectrum and on the cosmic coincidence problem.     

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.     

On the vanishing of the cosmological constant

A lagrangian is proposed for a Kaluza-Klein theory of gravity which has a vanishing cosmological constant as stable fixed point.     

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.     

Cosmological compactification in Kaluza-Klein model and time-dependent cosmological term

Einstein's equations for the generalized (4+D)-dimensional Robertson-Walker model are solved taking the conformally invariant action for the matter field. Compactification of this model is discussed and the compactification time/compactification mass scale for different values ofD is calculated. The resulting 4-dimensional action for gravity is obtained. It is found that a time-dependent cosmological constant is induced which is very large when the cosmic time is small and very small when the cosmic time is large.     

On the dynamics of cosmological particle production

The time evolution of the particle number density and spectrum of massive scalar particles, coupled conformally to a classical Friedman-Robertson-Walker gravitational field is followed numerically. Not only for a pure radiation cosmos, but also for one with an inflationary interlude, the density of particles produced remains constant in time. This results in a constant equivalent temperature scale up to the Compton time of the massive particles, and opens the possibility that during a sufficiently long inflation the energy density of the particles produced can exceed that of the radiation background.