Search Results (31)

We have analyzed solutions of bound states of a scalar particle in spacetime with torsion. In the first analysis, we investigate the confinement of a scalar particle in a cylindrical shell. In the second step, we investigate the Klein–Gordon oscillator. Then, we finish our analysis by searching for solutions of bound states of the Klein–Gordon oscillator by interacting with a hard-wall potential. In all these systems, we determine the relativistic energy profile in the background characterized by the presence of torsion in spacetime represented by a spiral-like dislocation. Full article

Alternative scenarios where the Big Bang singularity of the standard cosmological model is replaced by a bounce, or by an early almost static phase (known as emergent universe) have been frequently studied. We investigate the role of the spinor degrees of freedom in overcoming the initial singularity. We introduce a model which generalizes the Einstein–Cartan–Dirac theory, including local phase invariance of the spinor field supported by a gauge scalar field and certain couplings to the torsion. A natural gauge choice reduces the field equations to that of the Einstein–Dirac theory with a Dirac field potential that has polar and axial spinor currents. We identify a new potential term proportional to the square of the ratio of Dirac scalar and axial scalar, which provides a dark energy contribution dominating in the late-time Universe. In addition, the presence of spinor currents in the potential may induce the bounce of a contracting universe. Full article

The aim of this work is to demonstrate that all linear derivatives of the tensor algebra over a smooth manifold M can be viewed as specific cases of a broader concept—the operation of derivation. This approach reveals the universal role of differentiation, which simplifies and generalizes the study of tensor derivatives, making it a powerful tool in Differential Geometry and related fields. To perform this, the generic derivative is introduced, which is defined in terms of the quantities $Q_k^{\left(i\right)}\left(X\right)$. Subsequently, the transformation law of these quantities is determined by the requirement that the generic derivative of a tensor is a tensor. The quantities $Q_k^{\left(i\right)}\left(X\right)$ and their transformation law define a specific geometric object on M, and consequently, a geometric structure on M. Using the generic derivative, one defines the tensor fields of torsion and curvature and computes them for all linear derivatives in terms of the quantities $Q_k^{\left(i\right)}\left(X\right)$. The general model is applied to the cases of Lie derivative, covariant derivative, and Fermi derivative. It is shown that the Lie derivative has non-zero torsion and zero curvature due to the Jacobi identity. For the covariant derivative, the standard results follow without any further calculations. Concerning the Fermi derivative, this is defined in a new way, i.e., as a higher-order derivative defined in terms of two derivatives: a given derivative and the Lie derivative. Being linear derivative, it has torsion and curvature tensor. These fields are computed in a general affine space from the corresponding general expressions of the generic derivative. Applications of the above considerations are discussed in a number of cases. Concerning the Lie derivative, it is been shown that the Poisson bracket is in fact a Lie derivative. Concerning the Fermi derivative, two applications are considered: (a) the explicit computation of the Fermi derivative in a general affine space and (b) the consideration of Freedman–Robertson–Walker spacetime endowed with a scalar torsion field, which satisfies the Cosmological Principle and the computation of Fermi derivative of the spatial directions defining a spatial frame along the cosmological fluid of comoving observers. It is found that torsion, even in this highly symmetric case, induces a kinematic rotation of the space axes, questioning the interpretation of torsion as a spin. Finally it is shown that the Lie derivative of the dynamical equations of an autonomous conservative dynamical system is equivalent to the standard Lie symmetry method. Full article

We perform observational confrontation and cosmographic analysis of $f(T,T_G)$ gravity and cosmology. This higher-order torsional gravity is based on both the torsion scalar, as well as on the teleparallel equivalent of the Gauss–Bonnet combination, and gives rise to an effective dark-energy sector which depends on the extra torsion contributions. We employ observational data from the Hubble function and supernova Type Ia Pantheon datasets, applying a Markov chain Monte Carlo sampling technique, and we provide the iso-likelihood contours, as well as the best-fit values for the parameters of the power-law model, an ansatz which is expected to be a good approximation of most realistic deviations from general relativity. Additionally, we reconstruct the effective dark-energy equation-of-state parameter, which exhibits a quintessence-like behavior, while in the future the Universe enters into the phantom regime, before it tends asymptotically to the cosmological constant value. Furthermore, we perform a detailed cosmographic analysis, examining the deceleration, jerk, snap, and lerk parameters, showing that the transition to acceleration occurs in the redshift range $0.52\le z_{tr}\le 0.89$, as well as the preference of the scenario for quintessence-like behavior. Finally, we apply the Om diagnostic analysis to cross-verify the behavior of the obtained model. Full article

A natural connection with torsion is defined, and it is called the first natural connection on the Riemannian Π-manifold. Relations between the introduced connection and the Levi–Civita connection are obtained. Additionally, relations between their respective curvature tensors, torsion tensors, Ricci tensors, and scalar curvatures in the main classes of a classification of Riemannian Π-manifolds are presented. An explicit example of dimension five is provided. Full article

We consider a cosmological model in the framework of Einstein–Cartan theory with a single scalar torsion $\varphi =\varphi \left(t\right)$ and reconstruct the torsion model corresponding to the holographic dark energy (HDE) density. By studying the corresponding relation between the effective energy density of torsion field ${\rho }_{\varphi }$ and holographic dark energy density ${\rho }_{HDE}$, we naturally obtain a kind of torsion field from the interacting holographic dark energy with interaction term $Q=-2\varphi {\rho }_m$ and ${\rho }_m$ is the energy density of matter. We analyze the reconstructed torsion model and find that the torsion field behaves like the quintessence $(w>-1)$ or quintom (exhibiting a transition from $w>-1$ to $w<-1$) dark energy, depending on the value of the model parameter c. We then perform a stability analysis according to the squared sound speed. It is shown that the model is classically stable in the current epoch for the case of $c<1$. We also investigate the model from the viewpoint of statefinder parameters and it turns out that the statefinder trajectories in the $r-s$ plane behave differently for the three cases of c and also quite distinct from those of other cosmological models. From the trajectories of the statefinder pair $\{q,r\}$, we find that, for all the three cases of c, the universe has a phase transition from deceleration to acceleration, consistently with cosmological observations. In addition, we fit the reconstructed torsion model with the recent Type Ia supernovae (SNe Ia) samples, i.e., the Pantheon sample containing 1048 SNe Ia with the redshift in the range $0.01<z<2.3$ and the Pantheon+ sample with 1701 light curves of 1550 distinct SNe Ia in the range $0.001<z<2.26$. The analysis results show that the limits on the present fractional energy density of matter ${\Omega }_{m0}$ are completely compatible with those of the $\Lambda$CDM model obtained from the latest Planck mission observations at 68% confidence level. The mean value of c constrained from the Pantheon sample corresponds to the quintom-like scenario (i.e., $c<1$) and its mean value from the Pantheon+ sample corresponds to the quintessence-like scenario (i.e., $c\ge 1$). However, both of the Pantheon and Pantheon+ samples cannot distinguish the quintom-like and quintessence-like scenarios at 68% confidence level. Full article

We consider scalar-torsion gravity theories based on the exact solutions of a physical type of potential for cosmological inflationary models based on the non-minimal coupling of a scalar field and torsion. We analyzed the inflationary models with different types of inflationary dynamics and corresponding scalar field parameters. Such an approach allows us to consider different physical potentials and types of scalar-torsion gravity theories in the context of the realization of both stages of accelerated expansion of the universe. We also considered the correspondence surrounding the proposed inflationary models and the observational constraints on the parameters of cosmological perturbations. Full article

We confront $f(T,T_G)$ gravity, with big bang nucleosynthesis (BBN) requirements. The former is obtained using both the torsion scalar, as well as the teleparallel equivalent of the Gauss–Bonnet term, in the Lagrangian, resulting to modified Friedmann equations in which the extra torsional terms constitute an effective dark energy sector. We calculate the deviations of the freeze-out temperature $T_f$, caused by the extra torsion terms in comparison to $\Lambda$CDM paradigm. Then, we impose five specific $f(T,T_G)$ models and extract the constraints on the model parameters in order for the ratio $|\Delta T_f/T_f|$ to satisfy the observational BBN bound. As we find, in most of the models the involved parameters are bounded in a narrow window around their general relativity values as expected, asin the power-law model, where the exponent n needs to be $n\lesssim 0.5$. Nevertheless, the logarithmic model can easily satisfy the BBN constraints for large regions of the model parameters. This feature should be taken into account in future model building. Full article

The paper undertakes certain special forms of the quarter symmetric metric and non-metric connections on an $\epsilon$-anti-Kähler manifold. Firstly, we deduce the relation between the Riemannian connection and the special forms of the quarter symmetric metric and non-metric connections. Then, we present some results concerning the torsion tensors of these connections. In addition, we find the forms of the curvature tensor, the Ricci curvature tensor and scalar curvature of such connections and we search the conditions for the $\epsilon$-anti-Kähler manifold to be an Einstein space with respect to these connections. Finally, we study $U(Ric)$-vector fields with respect to these connections and give some results related to them. Full article

We investigate the Cartan formalism in $F\left(R\right)$ gravity. $F\left(R\right)$ gravity has been introduced as a theory to explain cosmologically accelerated expansions by replacing the Ricci scalar R in the Einstein–Hilbert action with a function of R. As is well-known, $F\left(R\right)$ gravity is rewritten as a scalar–tensor theory by using the conformal transformation. Cartan $F\left(R\right)$ gravity is described based on the Riemann–Cartan geometry formulated by the vierbein-associated local Lorenz symmetry. In the Cartan formalism, the Ricci scalar R is divided into two parts: one derived from the Levi–Civita connection and the other from the torsion. Assuming the spin connection-independent matter action, we have successfully rewritten the action of Cartan $F\left(R\right)$ gravity into the Einstein–Hilbert action and a scalar field with canonical kinetic and potential terms without any conformal transformations. red Thus, symmetries in Cartan $F\left(R\right)$ gravity are clearly conserved. The resulting scalar–tensor theory is useful in applications of the usual slow-roll scenario. As a simple case, we employ the Starobinsky model and evaluate fluctuations in cosmological microwave background radiation. Full article

Minisuperspace Quantum Cosmology is an approach by which it is possible to infer initial conditions for dynamical systems which can suitably represent observable and non-observable universes. Here we discuss theories of gravity which, from various points of view, extend Einstein’s General Relativity. Specifically, the Hamiltonian formalism for $f\left(R\right)$, $f\left(T\right)$, and $f\left(\mathcal{G}\right)$ gravity, with R, T, and $\mathcal{G}$ being the curvature, torsion and Gauss–Bonnet scalars, respectively, is developed starting from the Arnowitt–Deser–Misner approach. The Minisuperspace Quantum Cosmology is derived for all these models and cosmological solutions are obtained thanks to the existence of Noether symmetries. The Hartle criterion allows the interpretation of solutions in view of observable universes. Full article

In this brief paper, we show that atom interferometer experiments such as MAGIS, AION and AEDGE do not only have the potential to probe very light dark matter models, but will also probe quantum gravity. We show that the linear coupling of a singlet scalar dark matter particle to electrons or photons is already ruled out by our current understanding of quantum gravity coupled to data from torsion pendulum experiments. On the other hand, the quadratic coupling of scalar dark matter to electrons and photons has a large viable parameter space which will be probed by these atom interferometers. Implications for searches of quantum gravity are discussed. Full article

It is shown that the inflationary model is the result of the symmetry of the generalized $F(R,T,X,\phi )$-cosmological model using the Noether symmetry. It leads to a solution, a particular case of which is Starobinsky’s cosmological model. It is shown that even in the more particular case of cosmological models $F(R,X,\phi )$ and $F(T,X,\phi )$ the Monge–Ampère equation is still obtained, one of the solutions including the Starobinsky model. For these models, it is shown that one can obtain both power-law and exponential solutions for the scale factor from the Euler–Lagrange equations. In this case, the scalar field $\phi$ has similar time dependences, exponential and exponential. The resulting form of the Lagrangian of the model allows us to consider it as a model with $R^2$ or $X^2$. However, it is also shown that previously less studied models with a non-minimal relationship between R and X are important, as one of the possible models. It is shown that in this case the power-law model can have a limited evolutionary period with a negative value of the kinetic term. Full article

The paper presents the results of the analysis of the microstructure, mechanical properties, acoustic and magnetic characteristics of the metal of pipelines that are part of heat and power equipment, after long-term operation, made of structural and heat-resistant steels in the zones of localization of plastic deformation. Samples of 0.2 C steel and 0.12C-1Cr-1Mo-1V steel were studied in the initial state, as well as after operation for 219 and 360 thousand hours, respectively. As a result of the studies carried out for each sample, the phase composition was determined (qualitatively and quantitatively), and the following parameters of the fine structure were calculated: volume fractions of structural components of steel (pearlite and ferrite), scalar ρ and excess ρ± dislocation density, curvature-torsion of the crystal lattice χ, amplitude of internal stresses (shear stress and long-range stresses). All quantitative parameters of the structure are determined both in each structural component of steel, and in general for each sample. The structure of the metal of all specimens after deformation before the formation of zones of stable localization of deformations consists of a ferrite-pearlite mixture, and for specimens after operation before fracture only of unfragmented and fragmented ferrite. Ferrite, which occupies the bulk of the material, is present both unfragmented and fragmented. For all samples, the ratios ρ ≥ ρ_±, χ = χ_pl, σ_L ≥ σ_d were calculated, which indicate whether there is a danger of the initiation of microcracks in metal samples. For specimens without operation and after operation without damage in zones of stable localization of deformations, these conditions are met, and for specimens after operation until destruction, they are not met. It was found that the structural-phase state in the zones of localization of deformations has a direct effect on the characteristics of non-destructive tests. Thus, for all investigated samples, the values of such parameters as the delay time of the surface acoustic wave, the attenuation coefficient, the amplitude of the received signal, and the intensity of magnetic noise in the zones of deformation localization were established. Full article

We derive the full set of field equations for the metric-affine version of the Myrzakulov gravity model and also extend this family of theories to a broader one. More specifically, we consider theories whose gravitational Lagrangian is given by $F(R,T,Q,\mathcal{T},\mathcal{D})$ where T, Q are the torsion and non-metricity scalars, $\mathcal{T}$ is the trace of the energy-momentum tensor and $\mathcal{D}$ the divergence of the dilation current. We then consider the linear case of the aforementioned theory and, assuming a cosmological setup, we obtain the modified Friedmann equations. In addition, focusing on the vanishing non-metricity sector and considering matter coupled to torsion, we obtain the complete set of equations describing the cosmological behavior of this model along with solutions. Full article