Narrow Results

In this paper we investigate a universe filled with a fermionic field and a complex scalar field, exchanging energy through a Yukawa potential; the model encodes a symmetry breaking mechanism (on the bosonic sector). In the first case, when the mechanism is not included, the cosmological model furnishes a pure accelerated regime. In the second case, when including the symmetry breaking mechanism, we verify that the fermion and one of the bosons, of Higgs type, become massive, while the other boson is massless. Besides, the mechanism shows to be responsible for a transition from an accelerated to a decelerated regime, which certifies the importance, in cosmological terms, of its role. After symmetry breaking, the total pressure of the fields change its sign from negative to positive corresponding to the accelerated–decelerated transition. For large times, the universe becomes a dust (pressureless) dominated universe.

A cosmological model with a fermionic field and a massive bosonic field within the framework of the Einstein–Cartan theory is developed. The spacetime curvature is due to the matter-energy of the gravitational sources, whereas the torsion of the spacetime manifold follows from the spin density. From the numerical simulations it is shown that the fermionic spin density and the bosonic constituent answer for the transition from a decelerated to an accelerated era. The massive bosonic field behaves as dark energy, as it promotes the final accelerated period. During the initial decelerated era both constituents contribute, and the transition occurs as the torsion effect decreases with time. The exchange of energy between the constituents occurs via the gravitational field.

In this work, a model for the pre-inflationary universe is developed where the sources of the gravitational field are a relativistic fluid and a self-interacting fermionic field. The inclusion of the relativistic fluid is based on Schutz’s model. From the classical analysis based on the Hamiltonian formalism, it is shown that the fluid degrees of freedom can be embodied by a conformal time variable and an expression for the scale factor as function of the conformal time is obtained. From the Wheeler–DeWitt equation, the expected value for the scale factor as function of the conformal time is determined. It is shown that contrary to the classical solution, the expected value of the scale factor does not have a singularity, since it is preceded by a contracted phase up to a minimum value from which the universe begins to expand. Furthermore, from the plots of the classical and quantum solutions for the scale factor as functions of the conformal time it is shown that a decoherence of the quantum solution occurs for late times and both solutions coincide.

A model for an anisotropic pre-inflationary universe described by the Bianchi type-I metric is developed. A relativistic fluid of the Schutz formalism and a self-interacting fermionic field are considered as sources of the gravitational field. The classical analysis is based on the Hamiltonian formalism written in terms of the Misner variables and it is shown that the fluid degrees of freedom can be embodied by a conformal time variable. The three classical scale factors are obtained as functions of the conformal time. The quantum analysis follows from the de Broglie–Bohm formalism applied to the wave function which is a solution of the Wheeler–DeWitt equation and the three scale factors are also determined as functions of the conformal time. While the classical expressions for the scale factors show a singularity when the conformal time vanishes, their quantum expressions exhibit bouncing behavior. It is possible to adjust the behavior of the classical and quantum scale factors as functions of the conformal time so that they have a common isotropic behavior at late times with a dilution of the quantum effects.

We investigate the vacuum expectation value of the energy-momentum tensor associated with a massive fermionic field obeying the MIT bag boundary condition on a spherical shell in the global monopole spacetime. The asymptotic behavior of the vacuum densities is investigated near the sphere center and surface, and at large distances from the sphere. In the limit of strong gravitational field corresponding to small values of the parameter describing the solid angle deficit in global monopole geometry, the sphere-induced expectation values are exponentially suppressed.

In this work, a cosmological model inspired by string theory with Gauss–Bonnet term coupled to the fermionic field is taken into consideration. The self-interaction potential is considered as a combination of the scalar and pseudoscalar invariants. Here the cosmological contribution of the coupling of Gauss–Bonnet term with a non-Dirac fermionic field — characterized by an interaction term — is investigated. It is observed that the new type of coupling plays a significant role in the accelerating behavior of the universe. Specifically, in addition to the late time acceleration for the universe, produces an early decelerating behavior. The behavior of the equation-of-state parameter (w) is such that it guarantees the stability of the theory.

In this work, a cosmological model inspired by string/M-theory with fermionic field is taken into consideration. Here it is investigated whether the introduction of a non-Dirac fermionic field — characterized by an interaction term — affects the cosmological evolution. The self-interaction potential is considered as a combination of the scalar and pseudoscalar invariants. It is observed that the fermionic field under consideration behaves like an inflation field for the early universe and later on, as a dark energy field. The late time acceleration becomes more prominent by the addition of the interaction term. There is a slight decrease for the inflation peak as well as for the energy density. We see that the addition of higher-order terms to the fermionic part of Lagrangian does not significantly change either the inflation or the late time acceleration behavior.

A cosmological model for the early universe is investigated where a Schutz fluid and a fermionic field coupled to a gauge field are the sources of the gravitational field. The determination of the scale factor in the classical analysis follows from the Hamiltonian formulation together with Dirac’s method for constrained systems. The expectation value of the scale factor in the quantum analysis is determined from the Wheeler–DeWitt equation. The singularity in the classical solution for the scale factor is avoided in the quantum solution where a bouncing from a minimum value of the scale factor is present. It is shown that: (i) the minimum value of the scale factor depends on the ratio of the fermionic coupling constant and the mass of the vectorial field; (ii) the classical and quantum solutions coincide for large values of the conformal time due to a dilution of the quantum effects with the time evolution; (iii) the behavior of the wave function probability density confirms that the maximum probability occurs when the scale factor has its minimum value equal to its expectation value; (iv) the quantum potential in the Bohmian formulation goes to infinity when the scale factor tends to zero avoiding the singularity at this point.

We present a model of an early universe where the sources of gravitational effects are a scalar field, a relativistic fluid based on Schutz’s model and a self-interacting fermionic field. From the classical analysis based on the Hamiltonian formalism we show that the scale factor of the universe can be expressed in terms of a conformal time that emerges from the fluid’s degrees of freedom. From the Wheeler–DeWitt equation, a wave packet solution as function of the conformal time is determined. It is shown that the combination of the scalar and the fermionic field furnishes a consistent quantum regime and a smooth transition to the classical description, working with the aid of the Bohmian mechanics and in particular with the concept of quantum potential. The influence of the presence of the scalar field is also discussed.

In this work, I study the Casimir effect caused by a charged and massive scalar field that violates Lorentz symmetry in an aether-like and CPT even manner, by direct coupling between the field derivatives and two fixed orthogonal unit vectors. I call this a “double” Lorentz violation. The field will satisfy either Dirichlet or mixed boundary conditions on a pair of plane parallel plates. I use the generalized zeta function technique to examine the effect of a uniform magnetic field, perpendicular to the plates, on the Casimir energy and pressure. Three different pairs of mutual directions of the unit vectors are possible: timelike and spacelike perpendicular to the magnetic field, timelike and spacelike parallel to the magnetic field, spacelike perpendicular and spacelike parallel to the magnetic field. I fully examine all of them for both types of boundary conditions listed above and, in all cases and for both types of boundary conditions, I obtain simple expressions of the zeta function, Casimir energy and pressure in the three asymptotic limits of strong magnetic field, large mass, and small plate distance.

We calculate the vacuum averages of the energy–momentum tensor associated with a massless left-handed spinor fields due to magnetic fluxes on idealized cosmic string spacetime. In this analysis three distinct configurations of magnetic fields are considered: (i) a homogeneous field inside the tube, (ii) a magnetic field proportional to 1/r, and (iii) a cylindrical shell with δ-function. In these three cases the axis of the infinitely long tubes of radius R coincides with the cosmic string. In order to proceed with these calculations we explicitly obtain the Euclidean Feynman propagators associated with these physical systems. As we shall see, these propagators possess two distinct parts. The first are the standard ones, i.e. corresponding to the spinor Green's functions associated with the massless fermionic fields on the idealized cosmic string spacetime with a magnetic flux running through the line singularity. The second parts are new, they are due to the finite thickness of the radius of the tubes. As we shall see these extra parts provide relevant contributions to the vacuum averages of the energy–momentum tensor.

We investigate combined effects of nontrivial topology, induced by a cosmic string, and boundaries on the fermionic condensate and the vacuum expectation value (VEV) of the energy–momentum tensor for a massive fermionic field. As geometry of boundaries we consider two plates perpendicular to the string axis on which the field is constrained by the MIT bag boundary condition. By using the Abel–Plana type summation formula, the VEVs in the region between the plates are decomposed into the boundary-free and boundary-induced contributions for general case of the planar angle deficit. The boundary-induced parts in both the fermionic condensate and the energy–momentum tensor vanish on the cosmic string. Fermionic condensate is positive near the string and negative at large distances, whereas the vacuum energy density is negative everywhere. The radial stress is equal to the energy density. For a massless field, the boundary-induced contribution in the VEV of the energy–momentum tensor is different from zero in the region between the plates only and it does not depend on the coordinate along the string axis. In the region between the plates and at large distances from the string, the decay of the topological part is exponential for both massive and massless fields. This behavior is in contrast to that for the VEV of the energy–momentum tensor in the boundary-free geometry with the power law decay for a massless field. The vacuum pressure on the plates is inhomogeneous and vanishes at the location of the string. The corresponding Casimir forces are attractive.