International Journal of Geometric Methods in Modern Physics

The Barrow’s Holographic Dark Energy (BHDE) Model is proposed in an axially symmetric anisotropic spacetime which is employing Hubble horizon as an infrared cutoff (IR cutoff). The transition of the universe from a matter dominated era to a dark energy dominated era is investigated in this model. Furthermore, the Equation of State (EoS) parameter explains how the universe evolves with non-extensive term or Barrow parameter $\mathrm{\Delta }$ for both phase (i) phantom era (${\omega }_B\le -1$) and (ii) quintessence era (${\omega }_B\ge -1$). In order to reconcile the dark energy, the reconstruction of scalar field potential is considered. Some of the physical properties of the model are also described.

Using non-commutative spacetime quaternion algebra, we represent the generalization of one-dimensional and three-dimensional telegraph equations, which are widely applied to consider the propagation of an electromagnetic signal in communication lines, as well as to describe particle diffusion and heat transfer. It is shown that the system of telegraph equations can be represented in compact form as a single quaternion equation taking into account the spacetime properties of physical quantities. The distinctive features of the one-dimensional and three-dimensional telegraph equations are discussed.

This study is dedicated to investigate the Noether symmetry approach in a newly introduced gravitational theory known as $f(R,G,T)$ gravity, where $f$ is the function of Ricci scalar $R$, trace of energy–momentum tensor $T$, and the Gauss–Bonnet invariant term $G$. The Noether symmetry approach plays a supportive role in generating models and then determining the exact solutions by using the conserved quantities. For this purpose, the flat Friedmann–Robertson–Walker space–time is selected to observe cosmic evolution. The set of partial differential equations is calculated in the background $f(R,G,T)$ modified theory gravity. We further examine the four different $f(R,G,T)$ gravity models and calculate the conserved quantities to investigate the exact solutions. The three models show the increasing behavior of the cosmic scale factor that supports the expansion of universe. In fourth model, we are able to get the corresponding conserved quantity only and it is anticipated that this model will also support the expansion of universe.

This paper is devoted to analyzing a new model of a coupled Langevin system with fractional operators under nonlocal antiperiodic integral boundary conditions. This model involves nonlinear Langevin fractional equations with Caputo–Hadamard and Caputo fractional operators. Also, the existence and uniqueness of solutions to the suggested model have been investigated by the fixed-point technique. Moreover, the Hyers–Ulam stability of the solutions has been discussed. Finally, we provide an illustrative example to support the theoretical results.

In the de Broglie–Bohm interpretation of quantum mechanics, the momentum of a particle in a box of perfectly reflecting walls is vanishing. On the contrary, the classical physics predicts an oscillatory motion between the walls. The resulting difference between the behavior of a body in classical and quantum regime is unsatisfactory for Einstein and many other scientists. In order to solve the problem, we show that it is possible to obtain a motion of the body using the rules of quantum mechanics. The result holds for the quantum systems described by solutions of the time independent Schrödinger equation that are real functions.

In this paper, the discrete octonion linear canonical transform (DOCLCT) is presented. According to the definition of DOCLCT, its shift transform and modulation transform are explored. In addition, based on a new convolution operator, we obtain the convolution theorem of DOCLCT. The DOCLCT can be derived by the three-dimensional (3D) linear canonical transform. So, the fast algorithm of 3D DOCLCT is discussed. Finally, Heisenberg’s uncertainty principle associated with DOCLCT is established.

This paper considers the only sectors to constitute the present universe as the dark matter and dark energy. The proposed new agegraphic dark energy model studies the gradual transition from matter to dark energy in sequential order, including the current dominance of the matter sector by dark energy. The model utilizes concepts of Tsallis entropy and the Karolyhazy relation with conformal time $\eta$ as the time scale. Various evolutionary aspects of the universe are characterized by Tsallis parameter $\delta$ and the model constant $c$. Expressions for dynamic behavior of dark energy, as a differential equation, equation of state and deceleration parameters are obtained to describe the thermal history of universe evolution. Also, the stability of the model is analyzed through squared sound speed parameter. The analysis is made by considering an interaction as well as independence among the constituent sectors of the universe.

This work reports a study on bounce cosmology with a highly generalized holographic dark fluid inspired by Nojiri and Odintsov [Eur. Phys. J. C 77 (2017) 1–8]. The holographic dark fluid that is mostly used for late-time acceleration has been implemented to reconstruct toward realization of cosmological bounce. We first used the most generalized Nojiri–Odintsov (NO) cutoff to implement the holographic dark fluid. Accordingly, we have reconstructed this dark fluid via some solutions of scale factors. With those solutions, we have explored the evolution of different cosmological parameters. We have examined the effects of each reconstructed parameter in the context of the realization of the cosmic bounce. Next, we use the analytical inferences of the scalar spectral index, tensor-to-scalar ratio, and slow-roll characteristics of the model to study a bounce inflationary scenario. Since inflation is usually associated with the existence of scalar fields, we looked at a possible relationship between NO generalized holographic dark energy and scalar field models. Plotting the evolution of the potential results from the scalar fields against time. Finally, we investigated the GSL of thermodynamics in the pre- and post-bounce scenarios.

In this paper, we have explored cold dark matter and holographic dark energy cosmological model with big rip singularity. To obtain the solution of the field equation, we supposed that scalar expansion $𝜃$ is proportional to shear scalar ${\sigma }^2$, which leads to $P_1={(P_2)}^n$, where $P_1$, $P_2$ are metric potentials and $n$ is constant. Big bang and big rip singularity are investigated. The state-finder parameter is analyzed. The physical and geometrical parameters of the universe are explained.

This paper is devoted to the study of conformal and projective structures, and especially their connections, in the language of 2-frames, or $G$-structures of second order. While their normal Cartan connections are well-known, we use the dressing field method to obtain their local, mostly gauge invariant, connections. Lastly, we recall how to obtain the tractor bundle from conformal structures, and then show that we can define a projective tractor bundle using the same kind of construction.

This study deals with the time fractional 1D stochastic Poisson–Nernst–Planck (TFSPNP) system under the effect of multiplicative time noise. The M-truncated derivative (MTD) takes into consideration the fractional order time derivative. This is a steady-state Poisson–Nernst–Planck (PNP) equations that have applications in bioelectric dressings and bandages. To obtain the soliton solutions of TFSPNP, we use the generalized exponential rational functional method. These findings are presented in the form of trigonometric, exponential, and hyperbolic functions. Moreover, to show the effect of multiplicative time noise and MTD, we construct the plot of some solutions in the form of three-dimensional, two-dimensional, and their corresponding contours. These plots clearly show the effect of randomness in the wave structures for the exact solitary wave solutions that are attained. In general, the solutions become more stable when a noise term disrupts their symmetry.

Ever since new tetrads in four-dimensional Lorentzian curved spacetimes were introduced, many outstanding properties and results have been proven regarding Riemannian geometry, gauge theory or group theory. These tetrads might carry spacetime-kinematic information about particle multiplets. Among other properties, these new tetrads, locally and covariantly diagonalize stress–energy tensors. In the case where particles have an electromagnetic field, the local planes of gauge symmetry served as a tool in order to propose a new gravitational-kinematic interpretation of particle multiplets. The core reason stems from the mathematical fact that all local gauge symmetries associated to the Standard Model have been proven to be isomorphic to local groups of tetrad transformations in four-dimensional Lorentzian spacetimes. Therefore, the different stress–energy tensors have been proven to determine the local gauge geometry as a natural part of Riemannian geometry. The stress–energy tensors determine locally the orthogonal planes such that the rotation on either of them of the local tetrad vectors that span these planes is isomorphic to local tetrad gauge transformations. All these properties put together allow for a reinterpretation presented previously of particle states as particle gravitational-kinematic-spacetime tetrad states in the asymptotically flat limit. We proceed in this paper to study the case where there are $T$, $U$ and $V$ isospin subalgebras or submultiplets within the context of this new Riemannian interpretation of gauge symmetries.

In this work, the spherically symmetric wormhole solutions have been obtained in the four-dimensional Einstein–Gauss–Bonnet (4D EGB) gravity with isotropic and anisotropic matter sources. With each type of source, the traversable wormholes satisfying asymptotic flatness and flare-out conditions are developed. Further, the energy conditions explaining the nature of the matter in the interior of the wormhole are tested and the stability of wormhole solutions has been analyzed.

This paper examines the viable characteristics of anisotropic compact stars in $f(\Re ,T^2)$ theory ($\Re$ is the Ricci scalar and $T^2=T_{\alpha \beta }{T}^{\alpha \beta }$). In this perspective, we use Tolman–Kuchowicz solutions $(\mu =w{r}^2+2lnz$ and $\nu =ln(1+x{r}^2+y{r}^4))$ to examine the configurations of static spherically symmetric structures. The unknown constants are found by the first fundamental form of Darmois junction conditions. We analyze the behavior of fluid parameters in the interior of 4U 1538-52, PSRJ 1614-220, EXO 1785-248 and SAXJ 1808.4-3658 compact stars correspond to different models of this theory. Furthermore, the stability of the proposed compact stellar objects is examined through sound speed and adiabatic index methods. The satisfaction of requisite conditions ensures that stable compact objects exist in this framework.

This paper proposes a new model for anisotropic compact stars with quintessence in Rastall teleparallel gravity via embedding approach. In the gravity, the acquired field equations encompassing the anisotropic matter source as well as the quintessence field are studied using the specific character of the scalar torsion $T$ for the observed stars candidates PSRJ1416–2230, 4U1608–52, CenX–3, EXO 1785–248 and SMCX–1. All of the stellar structures under consideration are said to be advantageously independent of any central singularity and are stable. A thorough graphical analysis reveals that numerous physical properties critical for forming stellar structures are satisfied.

In this paper, we present the Noether symmetries of locally rotationally symmetric Bianchi-type I (LRS BI), an anisotropic model, in the context of the teleparallel gravity. We study a certain modified teleparallel theory based on the action that, in particular, contains a coupling between the scalar field and field strength (magnetism part). We derive the symmetry generators and show that, by means of cyclic variables approach, one can not obtain a suitable solution for field equations. Hence by the use of beyond Noether symmetry (B.N.S.) approach, we solve the equations which carry Noether currents as well. By data analysis of the obtained results, compatible results with observational data at the last half of the age of universe which is accelerating are demonstrated.

The matter–anti-matter asymmetry in the early Universe’s history is explained theoretically by the baryogenesis. It is well known that modified gravity theories are highly effective in explaining the Universe’s current accelerated state. In this paper, we examine the gravitational baryogenesis for $f(Q,C)$ gravity, where $Q$ is the non-metricity scalar and $C$ is the boundary term. To perform the baryogenesis, we assume linear, nonlinear and logarithmic forms of $f(Q,C)$. We evaluate the baryon-to-entropy ratio for our models by assuming the power law form of the scale factor $a(t)=a_0{t}^{\delta }$. We also investigate the generalized baryogenesis for our model by assuming the interaction term ${\partial }_{\mu }(Q+C)$. We constrain the model parameters by comparing with the observational value $\frac{{\eta }_B}{s}=9.42\times 10^{-11}$. Our derived models are physically viable.

Smooth and discontinuous (SD) oscillators are the nonlinear models that will exhibit SD dynamics due to continuous variation of the smooth parameter. Kosambi–Cartan–Chern (KCC) theory is a differential geometric theory that describes the deviations from the entire trajectory of the variational equation to the nearby trajectory. This paper presents a completely new dynamical analysis of a type of SD oscillators with nonlinear damping based on the KCC theory. First, the paper gives five KCC geometrical invariants of SD oscillators in the smooth and non-smooth cases, respectively. The results show that the geometric quantities in the non-smooth case cannot be derived directly from the geometric quantities in the smooth case. Second, from these geometric quantities, KCC stability of SD oscillators trajectory at any point except $x=0$ is analyzed. Lastly, numerical results show that in some regions that deviate from the equilibrium point of system, the system will exhibit complex and variable dynamical behavior due to small changes in parameters. This paper shows that the KCC theory is also a useful tool in the dynamical analysis of non-smooth systems.