Universe, Volume 6, Issue 12 (December 2020) – 25 articles

We introduce the supersymmetric version of YM-like theories with infinitely many spin fields in four dimensions. The construction is carried out via the superfield method. The surprising feature of these models is that they describe, in particular, gauge and gravity in a supersymmetric form, with no need for supergravity. Full article

We investigate the cosmological evolution of the power law k-essence dark energy (DE) model with interaction in FRWL spacetime with the Lagrangian that contains a kinetic function $F(X)=-\sqrt{X}+X$. Concretely, the cosmological evolution in this model are discussed by the autonomous dynamical system and its critical points, together with the corresponding cosmological quantities, such as ${\mathsf{\Omega }}_{\varphi }$, $w_{\varphi }$, $c_s^2$, and q, are calculated at each critical point. The evolutionary trajectories are drawn in order to show the dynamical process on the phases plan around the critical points. The result that we obtained indicates that there are four dynamical attractors, and all of them correspond to an accelerating expansion of universe for certain potential parameter and coupling parameter. Besides that, the geometrical diagnostic by the statefinder hierarchy $S_3^{(1)}$ and $S_4^{(1)}$ of this scalar field model are numerically obtained by the phase components, as an extended null diagnostic for the cosmological constant. This diagnostic shows that both the potential parameter $\lambda$ and interaction parameter $\alpha$ play important roles in the evolution of the statefinder hierarchy. Full article

General relativity has two fundamental problems that render it unsuitable for tackling the gravitational field’s quantization. The first problem is the lack of a genuine gravitational variable representing gravitation only, inertial forces apart. The second problem is its incompatibility with quantum mechanics, a problem inherited from the more fundamental conflict of special relativity with quantum mechanics. A procedure to overcome these difficulties is outlined, which amounts to replacing general relativity with its teleparallel equivalent and the Poincaré-invariant special relativity with the de Sitter-invariant special relativity. Those replacements give rise to the de Sitter-modified teleparallel gravity, which does not have the two mentioned problems. It can thus be considered an improved alternative approach to quantum gravity. Full article

In generic curved spacetimes, the unavailability of a natural choice of vacuum state introduces a serious ambiguity in the Fock quantization of fields. In this review, we study the case of fermions described by a Dirac field in non-stationary spacetimes, and present recent results obtained by us and our collaborators about well-motivated criteria capable to ensure the uniqueness in the selection of a vacuum up to unitary transformations, at least in certain situations of interest in cosmology. These criteria are based on two reasonable requirements. First, the invariance of the vacuum under the symmetries of the Dirac equations in the considered spacetime. These symmetries include the spatial isometries. Second, the unitary implementability of the Heisenberg dynamics of the annihilation and creation operators when the curved spacetime is treated as a fixed background. This last requirement not only permits the uniqueness of the Fock quantization but, remarkably, it also allows us to determine an essentially unique splitting between the phase space variables assigned to the background and the fermionic annihilation and creation variables. We first consider Dirac fields in 2 + 1 dimensions and then discuss the more relevant case of 3 + 1 dimensions, particularizing the analysis to cosmological spacetimes with spatial sections of spherical or toroidal topology. We use this analysis to investigate the combined, hybrid quantization of the Dirac field and a flat homogeneous and isotropic background cosmology when the latter is treated as a quantum entity, and the former as a perturbation. Specifically, we focus our study on a background quantization along the lines of loop quantum cosmology. Among the Fock quantizations for the fermionic perturbations admissible according to our criteria, we discuss the possibility of further restricting the choice of a vacuum by the requisite of a finite fermionic backreaction and, moreover, by the diagonalization of the fermionic contribution to the total Hamiltonian in the asymptotic limit of large wave numbers of the Dirac modes. Finally, we argue in support of the uniqueness of the vacuum state selected by the extension of this diagonalization condition beyond the commented asymptotic region, in particular proving that it picks out the standard Poincaré and Bunch–Davies vacua for fixed flat and de Sitter background spacetimes, respectively. Full article

In this paper we review results obtained in the searches of double beta decays to excited states of the daughter nuclei and illustrate the related experimental techniques. In particular, we describe in some detail the only two cases in which the transition has been observed; that is the $2{\beta }^{-}(0^{+}\to 0_1^{+})$ decay of ${}^{100}$Mo and ${}^{150}$Nd nuclides. Moreover, the most significant results in terms of lower limits on the half-life are also summarized. Full article

Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime geometries, providing the adequate formalism for metric-affine theories of gravity with curvature, torsion and non-metricity. In this paper, we analyze the structure of gauge theories of gravity and consider the relation between fundamental geometrical objects and symmetry principles as well as different spacetime paradigms. Special attention is given to Poincaré gauge theories of gravity, their field equations and Noether conserved currents, which are the sources of gravity. We then discuss several topics of the gauge approach to gravitational phenomena, namely, quadratic Poincaré gauge models, the Einstein-Cartan-Sciama-Kibble theory, the teleparallel equivalent of general relativity, quadratic metric-affine Lagrangians, non-Lorentzian connections, and the breaking of Lorentz invariance in the presence of non-metricity. We also highlight the probing of post-Riemannian geometries with test matter. Finally, we briefly discuss some perspectives regarding the role of both geometrical methods and symmetry principles towards unified field theories and a new spacetime paradigm, motivated from the gauge approach to gravity. Full article

Quaternions have an (over a century-old) extensive and quite complicated interaction with special relativity. Since quaternions are intrinsically 4-dimensional, and do such a good job of handling 3-dimensional rotations, the hope has always been that the use of quaternions would simplify some of the algebra of the Lorentz transformations. Herein we report a new and relatively nice result for the relativistic combination of non-collinear 3-velocities. We work with the relativistic half-velocities w defined by $v=\frac{2w}{1+w^2}$, so that $w=\frac{v}{1+\sqrt{1-v^2}}=\frac{v}{2}+\mathcal{O}\left(v^3\right)$, and promote them to quaternions using $\mathbf{w}=w\widehat{\mathbf{n}}$, where $\widehat{\mathbf{n}}$ is a unit quaternion. We shall first show that the composition of relativistic half-velocities is given by ${\mathbf{w}}_{1\oplus 2}\equiv {\mathbf{w}}_1\oplus {\mathbf{w}}_2\equiv {(1-{\mathbf{w}}_1{\mathbf{w}}_2)}^{-1}({\mathbf{w}}_1+{\mathbf{w}}_2)$, and then show that this is also equivalent to ${\mathbf{w}}_{1\oplus 2}=({\mathbf{w}}_1+{\mathbf{w}}_2){(1-{\mathbf{w}}_2{\mathbf{w}}_1)}^{-1}$. Here as usual we adopt units where the speed of light is set to unity. Note that all of the complicated angular dependence for relativistic combination of non-collinear 3-velocities is now encoded in the quaternion multiplication of ${\mathbf{w}}_1$ with ${\mathbf{w}}_2$. This result can furthermore be extended to obtain novel elegant and compact formulae for both the associated Wigner angle $\Omega$ and the direction of the combined velocities: ${\mathrm{e}}^{\mathbf{\Omega }}={\mathrm{e}}^{\Omega \widehat{\mathbf{\Omega }}}={(1-{\mathbf{w}}_1{\mathbf{w}}_2)}^{-1}(1-{\mathbf{w}}_2{\mathbf{w}}_1)$, and ${\widehat{\mathbf{w}}}_{1\oplus 2}={\mathrm{e}}^{\mathbf{\Omega }/2}\frac{{\mathbf{w}}_1+{\mathbf{w}}_2}{|{\mathbf{w}}_1+{\mathbf{w}}_2|}$. Finally, we use this formalism to investigate the conditions under which the relativistic composition of 3-velocities is associative. Thus, we would argue, many key results that are ultimately due to the non-commutativity of non-collinear boosts can be easily rephrased in terms of the non-commutative algebra of quaternions. Full article

We review the Montevideo Interpretation of quantum mechanics, which is based on the use of real clocks to describe physics, using the framework that was recently introduced by Höhn, Smith, and Lock to treat the problem of time in generally covariant systems. These new methods, which solve several problems in the introduction of a notion of time in such systems, do not change the main results of the Montevideo Interpretation. The use of the new formalism makes the construction more general and valid for any system in a quantum generally covariant theory. We find that, as in the original formulation, a fundamental mechanism of decoherence emerges that allows for supplementing ordinary environmental decoherence and avoiding its criticisms. The recent results on quantum complexity provide additional support to the type of global protocols that are used to prove that within ordinary—unitary—quantum mechanics, no definite event—an outcome to which a probability can be associated—occurs. In lieu of this, states that start in a coherent superposition of possible outcomes always remain as a superposition. We show that, if one takes into account fundamental inescapable uncertainties in measuring length and time intervals due to general relativity and quantum mechanics, the previously mentioned global protocols no longer allow for distinguishing whether the state is in a superposition or not. One is left with a formulation of quantum mechanics purely defined in quantum mechanical terms without any reference to the classical world and with an intrinsic operational definition of quantum events that does not need external observers. Full article

In this paper, we will describe the idea that dark matter partly consists of gravitational solitons (gravisolitons). The corresponding solution is valid for weak gravitational fields (weak field limit) with respect to a background metric. The stability of this soliton is connected with the existence of a special foliation and amazingly with the smoothness properties of spacetime. Gravisolitons have many properties of dark matter, such as no interaction with light but act on matter via gravitation. In this paper, we showed that the gravitational lensing effect of gravisolitons agreed with the lensing effect of usual matter. Furthermore, we obtained the same equation of state $w=0$ as matter. Full article

Neutrinoless double beta ($0\nu \beta \beta$) decay searches are currently among the major foci of experimental physics. The observation of such a decay will have important implications in our understanding of the intrinsic nature of neutrinos and shed light on the limitations of the Standard Model. The rate of this process depends on both the unknown neutrino effective mass and the nuclear matrix element ($M^{0\nu }$) associated with the given $0\nu \beta \beta$ transition. The latter can only be provided by theoretical calculations, hence the need of accurate theoretical predictions of $M^{0\nu }$ for the success of the experimental programs. This need drives the theoretical nuclear physics community to provide the most reliable calculations of $M^{0\nu }$. Among the various computational models adopted to solve the many-body nuclear problem, the shell model is widely considered as the basic framework of the microscopic description of the nucleus. Here, we review the most recent and advanced shell-model calculations of $M^{0\nu }$ considering the light-neutrino-exchange channel for nuclei of experimental interest. We report the sensitivity of the theoretical calculations with respect to variations in the model spaces and the shell-model nuclear Hamiltonians. Full article

Motivated by the recent discoveries of compact objects from LIGO/Virgo observations, we study the possibility of identifying some of these objects as compact stars made of dark matter called dark stars, or the mix of dark and nuclear matters called hybrid stars. In particular, in GW190814, a new compact object with 2.6 $M_{\odot }$ is reported. This could be the lightest black hole, the heaviest neutron star, and a dark or hybrid star. In this work, we extend the discussion on the interpretations of the recent LIGO/Virgo events as hybrid stars made of various self-interacting dark matter (SIDM) in the isotropic limit. We pay particular attention to the saddle instability of the hybrid stars which will constrain the possible SIDM models. Full article

The stage of a super-early (primordial) scale-invariant Universe is considered on the basis of the Poincaré–Weyl gauge theory of gravity in a Cartan–Weyl space-time. An approximate solution has been found that demonstrates an inflationary behavior of the scale factor and, at the same time, a sharp exponential decrease in the effective cosmological constant from a huge value at the beginning of the Big Bang to an extremely small (but not zero) value in the modern era, which solves the well-known “cosmological constant problem.” Full article

We revisit acceleration-induced nonlocal electrodynamics and the phenomenon of photon spin-rotation coupling. The kernel of the theory for the electromagnetic field tensor involves parity violation under the assumption of linearity of the field kernel in the acceleration tensor. However, we show that parity conservation can be maintained by extending the field kernel to include quadratic terms in the acceleration tensor. The field kernel must vanish in the absence of acceleration; otherwise, a general dependence of the kernel on the acceleration tensor cannot be theoretically excluded. The physical implications of the quadratic kernel are briefly discussed. Full article

We suggest two new scenarios of high-energy particle collisions in the background of a wormhole. In scenario 1, the novelty consists of the fact that the effect does not require two particles coming from different mouths. Instead, all such scenarios of high energy collisions develop, when an experimenter sends particles towards a wormhole from the same side of the throat. For static wormholes, this approach leads to indefinitely large energy in the center of mass. For rotating wormholes, it makes possible the super-Penrose process (unbounded energies measured at infinity). In scenario 2, one of colliding particles oscillates near the wormhole throat from the very beginning. In this sense, scenario 2 is intermediate between the standard one and scenario 1 since the particle under discussion does not come from infinity at all. Full article

We study the Jeans instability of an infinite homogeneous dissipative self-gravitating Bose–Einstein condensate described by generalized Gross–Pitaevskii–Poisson equations [Chavanis, P.H. Eur. Phys. J. Plus2017, 132, 248]. This problem has applications in relation to the formation of dark matter halos in cosmology. We consider the case of a static and an expanding universe. We take into account an arbitrary form of repulsive or attractive self-interaction between the bosons (an attractive self-interaction being particularly relevant for the axion). We consider both gravitational and hydrodynamical (tachyonic) instabilities and determine the maximum growth rate of the instability and the corresponding wave number. We study how they depend on the scattering length of the bosons (or more generally on the squared speed of sound) and on the friction coefficient. Previously obtained results (notably in the dissipationless case) are recovered in particular limits of our study. Full article

Neutrinoless double beta decay (DBD) is a useful probe to study neutrino properties such as the Majorana nature, the absolute neutrino mass, the CP phase and the others, which are beyond the standard model. The nuclear matrix element (NME) for DBD is crucial to extract the neutrino properties from the experimental transition rate. The neutrino-mass sensitivity, i.e., the minimum neutrino-mass to be measured by the DBD experiment, is very sensitive to the DBD NME. Actually, the NME is one of the key elements for designing the DBD experiment. Theoretical evaluation for the DBD NME, however, is very hard. Recently experimental studies of charge-exchange nuclear and leptonic reactions have shown to be used to get single-$\beta$ NMEs associated with the DBD NME. Critical discussions are made on the neutrino-mass sensitivity and the NME for the DBD neutrino-mass study and on the experimental studies of the single-$\beta$ NMEs and nuclear structures associated with DBD NMEs. Full article

We explore the potential offered by the incoming launch of the James Webb Space Telescope, to study the stars evolving through the asymptotic giant branch (AGB) phase. To this aim we compare data of AGB stars in the Large Magellanic Cloud, taken with the IRS spectrograph, with the results from modelling of AGB evolution and dust formation in the wind. We find that the best diagrams to study M- and C-stars are, respectively, ([F770W]−[F2500W], [F770W]) and ([F770W]−[F1800W], [F1800W]). ([F770W]−[F2500W], [F770W]) turns out to be the best way of studying the AGB population in its entirely. Full article

Neutron stars change their structure with accumulation of dark matter. We study how their mass is influenced from the environment. Close to the sun, the dark matter accretion from the neutron star does not have any effect on it. Moving towards the galactic center, the density increase in dark matter results in increased accretion. At distances of some fraction of a parsec, the neutron star acquire enough dark matter to have its structure changed. We show that the neutron star mass decreases going towards the galactic centre, and that dark matter accumulation beyond a critical value collapses the neutron star into a black hole. Calculations cover cases varying the dark matter particle mass, self-interaction strength, and ratio between the pressure of dark matter and ordinary matter. This allow us to constrain the interaction cross section, ${\sigma }_{\mathrm{dm}}$, between nucleons and dark matter particles, as well as the dark matter self-interaction cross section. Full article

In the Einstein–Cartan gravitational theory with the chameleon field, while changing its mass independently of the density of its environment, we analyze the Friedmann–Einstein equations for the Universe’s evolution with the expansion parameter a being dependent on time only. We analyze the problem of an identification of the chameleon field with quintessence, i.e., a canonical scalar field responsible for dark energy dynamics, and for the acceleration of the Universe’s expansion. We show that since the cosmological constant related to the relic dark energy density is induced by torsion (Astrophys. J.2016, 829, 47), the chameleon field may, in principle, possess some properties of quintessence, such as an influence on the dark energy dynamics and the acceleration of the Universe’s expansion, even in the late-time acceleration, but it cannot be identified with quintessence to the full extent in the classical Einstein–Cartan gravitational theory. Full article