Spinor fields in Bianchi type-I universe

A system of minimally coupled nonlinear spinor and scalar fields within the scope of a Bianchi type-I (BI) cosmological model in the presence of a perfect fluid and a cosmological constant (Λ term) is studied, and solutions to the corresponding field equations are obtained. The problem of initial singularity and the asymptotical isotropization process of the Universe are thoroughly studied. The effect of the Λ term on the character of evolution is analyzed. It is shown that some special choice of spinor field nonlinearity generates a regular solution, but the absence of singularity results in violating the dominant energy condition in the Hawking-Penrose theorem. It is also shown that a positive Λ, which denotes an additional gravitational force in our case, gives rise to an oscillatory or a non-periodic mode of expansion of the Universe depending on the choice of problem parameter. The regular oscillatory mode of expansion violets the dominant energy condition if the spinor field nonlinearity occurs as a result of self-action, whereas, in the case of a linear spinor field or nonlinear one that occurs due to interaction with a scalar field, the dominant condition remains unbroken. A system with time-varying gravitational (G) and cosmological (Λ) constants is also studied to some extent. The introduction of magneto-fluid in the system generates nonhomogeneity in the energy-momentum tensor and can be exactly solved only under some additional condition. Though in this case, we indeed deal with all four known fields, i.e., spinor, scalar, electromagnetic, and gravitational, the over-all picture of evolution remains unchanged.     

Scalar Gravity and Higgs Mechanism

The role that the auxiliary scalar field φ plays in Brans–Dicke cosmology is discussed. If a constant vacuum energy is assumed to be the origin of dark energy, then the corresponding density parameter would be a quantity varying with φ; and almost all of the fundamental components of our universe can be unified into the dynamical equation for φ. As a generalization of Brans–Dicke theory, we propose a new gravity theory with a complex scalar field ϕ which is coupled to the cosmological curvature scalar. Through such a coupling, the Higgs mechanism is naturally incorporated into the evolution of the universe, and a running density of the field vacuum energy is obtained which may release the particle standard model from the rigorous cosmological constant problem in some sense. Our model predicts a running mass scale of the fundamental particles in which the gauge symmetry breaks spontaneously. The running speed of the mass scale in our case could survive all existing experiments.     

Cosmological Implications of Interacting Polytropic Gas Dark Energy Model in Non-flat Universe

The polytropic gas model is investigated as an interacting dark energy scenario. The cosmological implications of the model including the evolution of EoS parameter w _Λ, energy density Ω_Λ and deceleration parameter q are investigated. We show that, depending on the parameter of model, the interacting polytropic gas can behave as a quintessence or phantom dark energy. In this model, the phantom divide is crossed from below to up. The evolution of q in the context of polytropic gas dark energy model represents the decelerated phase at the early time and accelerated phase later. The singularity of this model is also discussed. Eventually, we establish the correspondence between interacting polytropic gas model with tachyon, K-essence and dilaton scalar fields. The potential and the dynamics of these scalar field models are reconstructed according to the evolution of interacting polytropic gas.     

Interacting Spinor and Scalar Fields in Bianchi Type I Universe Filled with Perfect Fluid: Exact Self-Consistent Solutions

In the framework of Bianchi I (BI) cosmological models a self-consistent system of interacting spinor and scalar fields has been considered. We introduced an interaction function F(I, J) which is an arbitrary function of invariants I and J, generated from the real bilinear forms of the spinor field. Exact self-consistent solutions to the field equations have been obtained for the cosmological model filled with perfect fluid. The initial and the asymptotic behavior of the field functions and of the metric one has been thoroughly studied.     

A Quantum Cosmological Bianchi I Model with Interacting Spinor and Scalar Fields

A Bianchi I model of the Universe filled with interacting nonlinear spinor and scalar fields is studied within quantum geometrodynamics. Three types of interaction are considered: gradient, Yukawa, and axion ones. For massless fermion fields, the variables in the Wheeler – de Witt equation will separate. The solution can be interpreted using a two-component perfect liquid. One component corresponds to a massless scalar field, while the other – to a nonlinear spinor field. The interaction between the spinor and scalar fields can lead to elimination of singularity of the wave function. There is a possibility of existence of a discrete spectrum of the quantum Universe, as well as tunneling from the region with a rigorous equation of state to the region of the de Sitter vacuum.     

Rotating quantum cosmological models with wave fields

The quantum evolution of homogeneous rotating cosmological models of the Gödel type with spinor and scalar fields is considered within the framework of the formalism of superspace quantization. De Witt's equation for a rotating cosmological model is shown to take the form of a Schrödinger equation in which the role of time is played by the phase of the spinor field, and it becomes possible to determine correctly the probability that rotating models lacking an initial singularity exist.K. D. Ushinskii Yaroslav Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 41–44, January, 1993.     

Couplings of N=1 chiral spinor multiplets

We derive the action for n_L≥1 chiral spinor multiplets coupled to vector and scalar multiplets. We give the component form of the action, which contains gauge invariant mass terms for the antisymmetric tensors in the spinor superfield and additional Green–Schwarz couplings to vector fields. We observe that supersymmetry provides mass terms for the scalars in the spinor multiplet that do not arise from eliminating an auxiliary field. We construct the dual action by explicitly performing the duality transformations in superspace and give its component form.     

Exact self-consistent plane-symmetric solutions of the equations of two interacting fields (spinor field and scalar field)

A spinor field interacting with a zero-mass neutral scalar field is considered for the case of the simplest type of direct interaction, where the interaction Lagrangian has the formL _int =1/2 ϕ_αϕ_,α F(S) whereF(S) is an arbitrary function of the spinor field invariantS=ψψ. Exact solutions of the corresponding systems of equations that take into account the natural gravitational field in a plane-symmetric metric are obtained. It is proved that the initial system of equations has regular localized soliton-type solutions only if the energy density of the zero-mass scalar field is negative as it “disengages” from interaction with the spinor field. In two-dimensional space-time the system of field equations we are studying describes the configuration of fields with constant energy densityT ₀₀ , i.e., no soliton-like solutions exist in this case. Russian People’s Friendship University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 69–75, July, 1998.     

Bianchi Type-I Model with Cosmic String in the Presence of a Magnetic Field: Spinor Description

A Bianchi type-I cosmological model in the presence of a magnetic flux along a cosmic string is investigated. A nonlinear spinor field is used to simulate the cosmological cloud of strings. It is shown that the spinor field simulation offer the possibility to solve the system of Einstein’s equation without any additional assumptions. It is pointed out that the present model is nonsingular at the end of the evolution and does not allow the anisotropic Universe to turn into an isotropic one.     

Bianchi Type-V Cosmological Model with Two Interacting Scalar Fields

The open anisotropic cosmological model of the early Universe is considered. Two interacting scalar fields with special form of potential energy are a source of matter fields. Analytic solutions for inflationary and scalaron stages are found. The exact solutions to the corresponding field equations are obtained in quadrature form. The cosmological parameters have been discussed in detail and it is also shown that the solutions tend asymptotically to isotropic Friedmann-Robertson-Walker cosmological model.     

Spinors, Inflation, and Non-Singular Cyclic Cosmologies

We consider toy cosmological models in which a classical, homogeneous, spinor field provides a dominant or sub-dominant contribution to the energy-momentum tensor of a flat Friedmann-Robertson-Walker universe. We find that, if such a field were to exist, appropriate choices of the spinor self-interaction would generate a rich variety of behaviors, quite different from their widely studied scalar field counterparts. We first discuss solutions that incorporate a stage of cosmic inflation and estimate the primordial spectrum of density perturbations seeded during such a stage. Inflation driven by a spinor field turns out to be unappealing as it leads to a blue spectrum of perturbations and requires considerable fine-tuning of parameters. We next find that, for simple, quartic spinor self-interactions, non-singular cyclic cosmologies exist with reasonable parameter choices. These solutions might eventually be incorporated into a successful past- and future-eternal cosmological model free of singularities. In an Appendix, we discuss the classical treatment of spinors and argue that certain quantum systems might be approximated in terms of such fields.     

An Interacting Two-Fluid Scenario for Quintom Dark Energy

The Quintom dark energy is a proposal that explains the recent observations that mildly favor the equation of state of dark energy ω crossing -1 near the past. The Quintom model is often constructed by two scalar fields, where one is the quintessence feld and another is the phantom field. The cosmological implication of the coupling of the two fields of the dark energy is out of question worth investigating. However, the consideration of the coupling in the field scenario is somewhat complex thus we propose an interacting two-fluid Quintom scenario for simplicity. The interaction between the two components is parametrized by a constant 71 in this scenario. The cosmological implications of this parametrization are investigated in detail in this paper. Also, a diagnostic for this model is performed by using the statefinder pairs {s, r} and {q, r}.     

Gravitational and quantum effects in rotating cosmological models

Specific effects of the dynamics of (spinor and scalar) wave fields are considered in rotating uniform Gödel-type cosmological models. It is shown that the gravitational interaction of the spinor field can be reduced to the interaction between its pseudovector current and the angular velocity of space-time rotation and is similar to its interaction with the pseudotrace of the space-time twisting. The mean values of energy-momentum tensor of the quantized scalar field in vacuum are calculated in rotating cosmological models and the difference between these values and their mean counterparts in vacuum is determined for Friedman's nonrotating cosmological models.State Education Institute, Yaroslavl'. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 35–38, June, 1992.     

Space-time evolution induced by spinor fields with canonical and non-canonical kinetic terms

We study spinor field theories as an origin to induce space-time evolution. Self-interacting spinor fields with canonical and non-canonical kinetic terms are considered in a Friedman–Robertson–Walker universe. The deceleration parameter is calculated by solving the equation of motion and the Friedman equation, simultaneously. It is shown that the spinor fields can accelerate and decelerate the universe expansion. To construct realistic models we discuss the contributions from the dynamical symmetry breaking.     

Extended Einstein–Cartan theory à la Diakonov: The field equations

Diakonov formulated a model of a primordial Dirac spinor field interacting gravitationally within the geometric framework of the Poincaré gauge theory (PGT). Thus, the gravitational field variables are the orthonormal coframe (tetrad) and the Lorentz connection. A simple gravitational gauge Lagrangian is the Einstein–Cartan choice proportional to the curvature scalar plus a cosmological term. In Diakonov?s model the coframe is eliminated by expressing it in terms of the primordial spinor. We derive the corresponding field equations for the first time. We extend the Diakonov model by additionally eliminating the Lorentz connection, but keeping local Lorentz covariance intact. Then, if we drop the Einstein–Cartan term in the Lagrangian, a nonlinear Heisenberg type spinor equation is recovered in the lowest approximation.     

Polarization of vacuum of quantum fields in the Aaronov-Bohm external field. II

A spinor field interacting with the Aaronov-Bohm external field is examined. Analytical expressions for the vacuum average components of the energy-momentum tensor are derived. Dependences of the components of energymomentum tensor of the spinor field in the vacuum state on the distance and field strength are investigated. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 3–8, April, 2006.     

Stability Properties and Asymptotics for N Nonminimally Coupled Scalar Fields Cosmology

We consider here the dynamics of some homogeneous and isotropic cosmological models with N interacting classical scalar fields nonminimally coupled to the spacetime curvature, as an attempt to generalize some recent results obtained for one and two scalar fields. We show that a Lyapunov function can be constructed under certain conditions for a large class of models, suggesting that chaotic behavior is ruled out for them. Typical solutions tend generically to the empty de Sitter (or Minkowski) fixed points, and the previous asymptotic results obtained for the one field model remain valid. In particular, we confirm that, for large times and a vanishing cosmological constant, even in the presence of the extra scalar fields, the universe tends to an infinite diluted matter dominated era.     

Taming of divergences in a unitary model of massive fermions, vectors and scalars

We consider a massive vector field, interacting through three-field interactions with a massive scalar and spinor field, in a unitary model. There are divergences that cannot be removed by introduction of counter terms into the Lagrangian. It is shown that it is possible to tame many of them and to remove the remaining divergences by appropriate choices of the coupling constants.