Elko Field Research Articles

On the geometry and quantum theory of regular and singular spinors

We relate the Lounesto classification of regular and singular spinors to the orbits of the Spin(3,1) group in the space of Dirac spinors. We find that regular spinors are associated with the principal orbits of the spin group while singular spinors are associated with special orbits whose isotropy group is C. We use this to clarify some aspects of the classical and quantum theory of spinors restricted to a class in this classification. In particular, we show that the degrees of freedom of an ELKO field, which has been proposed as a candidate for dark matter, can be reexpressed as a Dirac field preserving locality. Alternatively after introducing the ELKO dual, it can be re-interpreted as four anticommuting Lorentz scalar fields with internal symmetry the spin representation of the Lorentz group. We also propose an interacting Lagrangian which can consistently describe all 6 classes of regular and singular spinors.

5D Elko spinor field non-minimally coupled to nonmetricity in f(Q) gravity

This paper aims to investigate the localization of the five-dimensional spinor field known as Elko (dual-helicity eigenspinors of the charge conjugation operator) by employing a Yukawa-like geometrical coupling in which the Elko field is non-minimally coupled to nonmetricity scalar Q. We adopt the braneworld scenarios in which the first-order formalism with sine-Gordon and linear superpotentials is employed to obtain the warp factors. A linear function supports the zero-mode trapping within the geometric coupling, leading to the same effective potential as the scalar field. Moreover, an exotic term must be added to obtain real-valued massive modes. Such modes are investigated through the Schrödinger-like approach.

Towards a gravitational and supergravitational Elko theory

We describe a possible and alternative route to connect gravity with Elko theory. Our approach is based on the possibility to introduce a totally antisymmetric gauge field in the generalized Elko field equation, which is an alternative extension of the Dirac field equation. The corresponding totally antisymmetric field strength ([Formula: see text]-form) is then associated with Grassmann–Plücker coordinates and therefore with a decomposable [Formula: see text]-form. We show that such a totally antisymmetric field strength can be considered as the square root of the Riemann tensor associated to a homogeneous space. Motivated by this result we conjecture that a full connection with Riemann geometry and therefore with general relativity must be possible if such a field strength is not decomposable. We also show how a supergravity version could arise from a generalization of the above ideas.

Introduction to localization of Elko spinor fields on branes

In 2004, Dharam Vir Ahluwalia and Daniel Grumiller discovered a dark matter candidate called Elko: spin one-half fermions with mass dimension one. These fermions are described by a spinorial Klein-Gordon formalism and very different from electrons or neutrinos. In this review, we give a brief introduction to the localization of Elko spinor fields on branes. First, we briefly review some brane-world theories and the localization of bulk matter fields on branes. Then, after a brief introduction to Elko spinor fields, we focus on the localization of Elko fields on branes in three cases: the free Elko fields, the Elko fields with Yukawa-like coupling, and finally, the Elko fields with non-minimal coupling.

The Casimir effect for the scalar and Elko fields in a Lifshitz-like field theory

In this work, we obtain the Casimir energy for the real scalar field and the Elko neutral spinor field in a field theory at a Lifshitz fixed point (LP). We analyze the massless and the massive case for both fields using dimensional regularization. We obtain the Casimir energy in terms of the dimensional parameter and the LP parameter. Particularizing our result, we can recover the usual results without LP parameter in (3 + 1) dimensions presented in the literature. Moreover, we compute the effects of the LP parameter in the thermal corrections for the massless scalar field.

Localization of Elko spinor fields in tachyonic de Sitter braneworld models

In this paper, we investigate the localization of a five-dimensional (5D) Elko spinor field in de Sitter tachyonic braneworld models. These branes are generated by gravity coupled to a tachyonic bulk scalar field and include a de Sitter cosmological background induced on the 3D-brane. Using Yukawa-type coupling mechanism we show that a free massless Elko spinor field cannot be localized on tachyonic de Sitter branes while massive Elko fields are localized if their bulk mass obeys an upper bound. Also by introducing a tachyonic function F(T) as Yukawa interaction term between the Elko spinor and the background tachyonic scalar field we find that localized massless zero modes are given in terms of general Heun functions. Furthermore, it is shown that employing a new derivative coupling term in the action of Elko spinor fields leads to the Elko field localization on tachyonic de Sitter branes.

The massive Elko spinor field in the de Sitter braneworld model

The Elko spinor field is a spin 1/2 fermionic quantum field with a mass dimension introduced as a candidate of dark matter. In this work, we study the localization of Elko fields on a de Sitter thick brane constructed by a canonical or phantom scalar field. By presenting the mass-independent potentials of Kaluza-Klein (KK) modes in the corresponding Schrödinger equations, it is shown that the Elko spinor field with a five- dimensional mass term can be localized on de Sitter branes. Also, by using a Yukawa type coupling term, we find that the Elko spinor field can be localized on this brane with a particular coupling constant. Furthermore, it is shown that the zero mode of the Elko field is localized on the de Sitter brane through a Yukawa geometrical coupling term.

Partition function for a mass dimension one fermionic field and the dark matter halo of galaxies

This work studies the finite temperature effects of a mass dimension one fermionic field, sometimes called Elko field. The equilibrium partition function was calculated by means of the imaginary time formalism and the result obtained was the same for a Dirac fermionic field, even though the Elko field does not satisfy a Dirac-like equation. The high and low temperature limits were obtained, and for the last case the degeneracy pressure due to Pauli exclusion principle can be responsible for the dark matter halos around galaxies to be greater than or of the same order of the galaxy radius. Also, for a light particle of about 1.0 eV and a density of just 1 particle per cubic centimeter, the value of the total dark matter mass due to Elko particles is of the same order of a typical galaxy. Such a result satisfactorily explains the dark matter as being formed just by Elko fermionic particles and also the existence of galactic halos that go beyond the observable limit.

Localization of massless Elko spinor fields on de Sitter thick branes

In this work, we investigate the localization of a five-dimensional (5D) free massless Elko spinor field on de Sitter thick branes that are generated by a canonical or phantom scalar field. It is shown that the zero mode of Elko field cannot be localized on the de Sitter brane. In order to circumvent this problem, we employ a nonminimal coupling term in the 5D Elko spinor field action and find that the Elko field can be localized on the de Sitter brane with this mechanism.

Evolution of the universe driven by a mass-dimension-one fermion field

This paper studies the evolution of the universe filled with a neutral mass-dimension-one fermionic field, sometimes called Elko. The numerical analysis of the coupled system of equations furnishes a scale factor growth and energy density evolution that correctly reproduce the inflationary phase of the universe. After that, assuming a mechanism of energy transference to ordinary matter, the initial conditions generated after inflation drives the radiation-dominated phase and also the subsequent dark-matter evolution, since the Elko field is a good dark-matter candidate. The energy density of the field at the end of inflation, at the end of the radiation phase and for the present time are in agreement with the standard model estimates. The analysis was performed with a potential containing a quadratic mass term plus a quartic self-interaction term, which follows naturally from the theory of mass-dimension-one fermions. Inflation occurs when the field makes a kind of transition around the Planck mass scale. The number of e-foldings during inflation was found to be strongly dependent on the initial conditions of the Elko field, as occurs in chaotic inflationary models. An upper limit to the Elko mass is estimated. A possible interpretation of the inflation as a consequence of a kind of Pauli exclusion principle is presented at the end.

Creation of mass dimension one fermionic particles in asymptotically expanding universe

In the present work we study the process of particle creation for mass dimension one fermionic fields (sometimes named Elko) as a consequence of expansion of the universe. We study the effect driven by an expanding background that is asymptotically Minkowski in the past and future. The differential equation that governs the time mode function is obtained for the conformal coupling case and, although its solution is nonanalytic, within an approximation that preserves the characteristics of the terms that break analyticity, analytic solutions are obtained. Thus, by means of Bogolyubov transformations technique, the number density of particles created is obtained, which can be compared to exact solutions already present in literature for scalar and Dirac particles. The spectrum of the created particles was obtained and it was found that it is a generalization of the scalar field case, which converges to the scalar field one when the specific terms concerning the Elko field are dropped out. We also found that lighter Elko particles are created in larger quantities than the Dirac fermionic particles. By considering the Elko particles as candidate to the dark matter in the universe, such result shows that there are more light dark matter (Elko) particles created by the gravitational effects in the universe than baryonic (fermionic) matter, in agreement to the standard model.

From inflation to recent cosmic acceleration: the fermionic Elko field driving the evolution of the universe

In this paper we construct the complete evolution of the universe driven by the mass dimension one dark spinor called Elko, starting with inflation, passing by the matter dominated era and finishing with the recent accelerated expansion. The dynamic of the fermionic Elko field with a symmetry breaking type potential can reproduce all phases of the universe in a natural and elegant way. The dynamical equations in general case and slow roll conditions in the limit H≪ mpl are also presented for the Elko system. Numerical analysis for the number of e-foldings during inflation, energy density after inflation and for present time and also the actual size of the universe are in good agreement with the standard model of cosmology. An interpretation of the inflationary phase as a result of Pauli exclusion principle is also possible if the Elko field is treated as an average value of its quantum analogue.

Casimir effect for Elko fields

The Casimir effect for mass dimension one fermion fields (sometimes called Elko) in (3 + 1) dimensions is obtained using Dirichlet boundary conditions. It is shown that the existence of a repulsive force is four times greater than the case of the scalar field. The precise reason for such differences are highlighted and interpreted, as well as the right parallel of the Casimir effect due to scalar and fermionic fields.

Exotic Elko on string-like defects in six dimensions

We analyse the trapping of eigenspinors of the charge conjugation operator with dual helicity (Elko), in thin and thick string-like models with codimension-2. Elko spinor fields describe mass-dimension-one fermions in four dimensions (and, correspondingly, mass-dimension-two fermions in six dimensions), that represent natural dark-matter prime candidates. This dark spinor has many applications, from particle physics to cosmology. On the other hand, six-dimensional brane-world models have, among other prominent features, the spontaneous confinement of free spin-1 fields and a mechanism that explains the mass hierarchy of fundamental fermions. In this paper, we use scalar couplings in order to confine the zero mode of Elko in six dimensions. Moreover, we use the Elko dark-spinor features to propose an exotic coupling in order to remove the complex-valued terms in the massive Kaluza-Klein modes. Hence, we show that six-dimensional models can resolve the main issues of Elko fields confinement presented in five dimensions.

Λ(t) cosmology induced by a slowly varying Elko field

In this work the exact Friedmann-Robertson-Walker equations for an Elko spinor field coupled to gravity in an Einstein-Cartan framework are presented. The torsion functions coupling the Elko field spin-connection to gravity can be exactly solved and the FRW equations for the system assume a relatively simple form. In the limit of a slowly varying Elko spinor field there is a relevant contribution to the field equations acting exactly as a time varying cosmological model Λ(t)=Λ*+3β H2, where Λ* and β are constants. Observational data using distance luminosity from magnitudes of supernovae constraint the parameters Ωm and β, which leads to a lower limit to the Elko mass. Such model mimics, then, the effects of a dark energy fluid, here sourced by the Elko spinor field. The density perturbations in the linear regime were also studied in the pseudo-Newtonian formalism.

Searching for Elko dark matter spinors at the CERN LHC

The aim of this paper is to explore the possibility of discovering a fermionic field with mass dimension one, the Elko field, in the Large Hadron Collider. Due to its mass dimension, an Elko can only interact either with Standard Model spinors and gauge fields at one-loop order or at tree level through a quartic interaction with the Higgs field. In this Higgs portal scenario, the Elko is a viable candidate to a dark matter constituent which has been shown to be compatible with relic abundance measurements from WMAP and direct dark matter searches. We propose a search strategy for this dark matter candidate in the channel [Formula: see text] at the [Formula: see text] LHC. We show the LHC potential to discover the Elko considering a triple Higgs–Elkos coupling as small as ~0.5 after 1 ab-1 of integrated luminosity. Some phenomenological consequences of this new particle and its collider signatures are also discussed.

A new approach on the stability analysis in ELKO cosmology

In this work it has been developed a new approach to study the stability of a system composed by an ELKO field interacting with dark matter, which could give some contribution in order to alleviate the cosmic coincidence problem. It is assumed that the potential which characterizes the ELKO field is not specified, but it is related to a constant parameter $\delta$. The strength of the interaction between matter and ELKO field is characterized by a constant parameter $\beta$ and it is also assumed that both ELKO field as matter energy density are related to their pressures by equations of state parameters $\omega_\phi$ and $\omega_m$, respectively. The system of equations is analysed by a dynamical system approach. It has been found the conditions of stability between the parameters $\delta$ and $\beta$ in order to have stable fixed points for the system for different values of the equation of state parameters $\omega_\phi$ and $\omega_m$, and the results are presented in form of tables. The possibility of decay of ELKO field into dark matter or vice versa can be read directly from the tables, since the parameters $\delta$ and $\beta$ satisfy some inequalities. It allows us to constrain the potential assuming that we have a stable system for different interactions terms between the ELKO field and dark matter. The cosmic coincidence problem can be alleviated for some specific relations between the parameters of the model.

ELKO applications in cosmology

A brief review is presented about the ELKO spinor field applied to cosmology, with the main results and limitations of the theory. As a simple application, we have analyzed a model involving the interaction of the ELKO spinor field with dark matter in the universe from a dynamical system approach. When the system is rewritten in terms of the deceleration parameter q and under the assumption that such parameter is nearly constant for some different stages of the evolution, stability points were found for different types of interaction between dark matter and ELKO spinors. Within this new analysis several interesting scenarios are possible, depending on the interaction term. For example, if it is assumed that the equation of the state parameter of the ELKO field is of the phantom type, ωϕ < -1, the current acceleration of the universe can be driven by the decay of dark matter particles into ELKO field. Furthermore, even for ωϕ > 0, the inflationary period can be driven by the decay of the inflaton field (described by the ELKO spinor) into dark matter particles.

Perspectives for an Elko phenomenology using monojets at the 14 TeV LHC

The aim of this work is to explore the possibility to discover a fermionic field with mass dimension one, the Elko field, in the 14 TeV Large Hadron Collider (LHC), in processes with missing energy and one jet. We explore the possibility of a triple coupling with the Higgs field, generating also a contribution to the Elko mass term, and suggest some possibilities for future studies in this field.

Some remarks on the attractor behaviour in ELKO cosmology

Recent results on the dynamical stability of a system involving the interaction of the ELKO spinor field with standard matter in the universe have been reanalysed, and the conclusion is that such system does not exhibit isolated stable points that could alleviate the cosmic coincidence problem. When a constant parameter δ related to the potential of the ELKO field is introduced in the system however, stable fixed points are found for some specific types of interaction between the ELKO field and matter. Although the parameter δ is related to an unknown potential, in order to satisfy the stability conditions and also that the fixed points are real, the range of the constant parameter δ can be constrained for the present time and the coincidence problem can be alleviated for some specific interactions. Such restriction on the ELKO potential opens possibility to apply the ELKO field as a candidate to dark energy in the universe, and so explain the present phase of acceleration of the universe through the decay of the ELKO field into matter.