International Journal of Geometric Methods in Modern Physics

We review an algorithm, in the context of gauge and gravity theories described by differential forms, to read off the symmetries of a physical system out of its action, which was originally proposed in [C. Corral and Y. Bonder, Symmetry algebra in gauge theories of gravity, Class. Quantum Grav. 36 (2019) 045002]. In particular, we study the interplay between gauge symmetries and a gauge-covariant version of diffeomorphisms dubbed local translations. We focus on the role of boundary terms and conserved charges that were not discussed in the original proposal. We provide a review of the formalism and analyze several examples of classical theories, including gauge theories coupled to matter fields in flat space and gravitational theories in different dimensions.

The present exploration studies the dynamical profile, multistability and soliton solution of ion-acoustic waves (IAWs) in plasma physics. The new auxiliary equation approach is implemented to compute a wide range of solitary wave structures of different types. The dynamical profile is studied by using the bifurcation theory. This system is converted into a planar dynamical system via the Galilean transformation. Taking different cases of its coefficients, the phase plane analysis of this resultant dynamical system is performed. The phase diagrams show the different characteristics of the equilibrium points of the planar dynamical system. The quasi-periodic behaviors, multistability of this planar dynamical system are done by adding the perturbation term. The sensitivity assessment of this perturbed dynamical system is performed by taking different initial constraints.

A cosmological model is described in this study using $f(Q,T)$ gravity, and the parameters are restricted using cosmological data sets. We start out by using a well-motivated form of $f(Q,T)$ as $f(Q,T)=mQ+nT$, where $m$ and $n$ are model parameters. To solve the field equations, we use the relation that the deceleration parameter is inversely related to the Hubble parameter. In this case, we find that by parametrizing the cosmological parameters the transition redshift between early deceleration and late time acceleration occurs at $z_t=0.453_{-0.0017}^{+0.0017}$ The positive slope of the Om $(z)$ diagnostic analysis indicates that the model is in a phantom phase. Based on the current study, it seems that $f(Q,T)$ gravity might offer a substitute for dark energy in order to address the current cosmic acceleration.

The purpose of this paper is to study the feasibility and the appearance of charged thin-shell wormholes using generalized Chaplygin gas under the influence of minimally coupled $f(R,T)$ gravitational theory. Here, $f$ is a generic function of the scalar curvature $R$ and the trace of stress-energy tensor $T$. We explore different components of Lanczos equations in the context of a specific $f(R,T)$ functional form, i.e. $f(R,T)=R+2\lambda T$, by applying junction conditions on field equations. We study static stable solutions using radial perturbation and the generalized Chaplygin gas equation of state (EoS) with the isotropic environment. We investigate the stable (unstable) static wormhole solutions for various physical parametric values and illustrate them graphically.

This paper characterizes $(m,\rho )$-quasi-Einstein solitons on $3$-dimensional trans-Sasakian manifolds. It has been shown that a closed $(m,\rho )$-quasi-Einstein soliton on a $3$-dimensional trans-Sasakian manifold is either cosymplectic or Einstein under certain restrictions. Moreover, we investigate $(m,\rho )$-quasi-Einstein solitons with certain potential vector fields on $3$-dimensional trans-Sasakian manifolds. As an application of this soliton, we also analyze super quasi-Einstein spacetimes whose metrics are associated with $(m,\rho )$-quasi-Einstein solitons.

The prediction about the accelerating expansion of the universe introduced the concept of dark energy. Since then, a plethora of work has been done to explain the origin and nature of dark energy. This work deals with the possibility of obtaining cosmic acceleration of a new kind of dark energy, viz., Yang–Mills condensate dark energy in generalized Brans–Dicke theory with variable or constant $\omega$ (Brans–Dicke parameter) and vanishing and non-vanishing self-interacting potential. We assume the scale factor and scalar field in power law form. Then we investigate the above model to determine whether the universe is accelerating. We obtain a redshift-dependent equation of state parameter, which describes the phase transition of the universe. We notice that the equation of the state parameter meets the $\mathrm{\Lambda }$ cold dark matter (CDM) limit in the far future. Then we study the $w_D-w_D^{\prime }$ analysis to get the thawing or freezing region. We study the stability of the model by studying the square speed of sound. Last, the nature of the scalar field and the potential are analyzed for four cases.

This paper explores the quintessence reconstruction and statefinder perspective of Kaniadakis holographic dark energy model in a flat universe with future event horizon as an IR-cutoff. The cosmological parameters of this model were re-examined from the quintessence behavior aspect. Also we reconstruct, $V({\varphi }_Q)$, the potential of quintessence scalar field, which shows the best fit with joint analysis data of JLA+CC+BAO for the priors $H_0=69.6\pm 0.7$, $H_0=73.24\pm 1.74$. In the $w_{\mathrm{\text{DE}}}$–${ẁ}_{\mathrm{\text{DE}}}$ phase space, the freezing-tracker model represents our canonical scalar field. This model exhibits quintessence behavior in the statefinder ($r$–$s$) plane for model parameters $c$ and $\beta$ that are close to $1$ and $0$. The present values of deceleration $q_0$, statefinder $(r_0,s_0)$, jerk $j_0$ and model parameters $\beta ,c$ are consistent with the limits of the observational data. Using the distance modulus $\mu$, we also fit 580 SN Type I Union2.1 data sets to our model.

In this paper, we establish two Kastler–Kalau–Walze type theorems for conformal perturbations of modified Novikov operators on four-dimensional and six-dimensional compact manifolds with (respectively, without) boundary.

In this paper, we study classification of magnetic curves corresponding to Killing vector fields of ${ℍ}^3$. First, we solve the geodesic equation analytically. Then we calculate the trajectories generated by all the six Killing vector fields, which are considered as magnetic field vectors, by using perturbation method up to first-order with respect to the strength of the magnetic field. We present a comparison of our solution with the numerical solution for one case. We also prove that 3-dimensional $(\alpha )$-Kenmotsu manifolds cannot have any magnetic vector field in the direction of their Reeb vector fields.

In this paper, we further investigate the cosmological tests of the deceleration parameter $q=\alpha -\frac{\beta }{H}$ with $f(T)=\kappa +\lambda T$, where $\kappa$ and $\lambda$ are free parameters in $f(t)$ framework by using 31 measurements from CC datasets, 1048 measurements of type Ia Supernovae (SNeIa) and 17 uncorrelated BAO measurements using Markov Chain Monte Carlo (MCMC). We obtained the best fit value of our model parameter and obtain the cosmological parameters of our model and analysis cosmographic studies of model. The statistical analysis revealed that our model is supported by the current Universe.

In this work, we apply the extended constant-roll condition to non-canonical scalar fields. We use in particular two types of non-canonical fields, namely, the tachyon field and the Dirac–Born–Infeld (DBI) field. We assume, in particular, that the tachyon scalar field satisfies the condition $\ddot{\varphi }=\alpha (\varphi )V^{\prime }(\varphi )/V(\varphi )$, while the DBI scalar field satisfies the condition $\ddot{\varphi }=\alpha (\varphi )V^{\prime }(\varphi )$. We use the extended constant-roll condition to calculate the inflation indices for each of these non-canonical fields. In order to test the extended constant-roll condition, we use three types of potentials, namely chaotic potential, linear power-law potential and exponential potential, and choose power-law and exponential forms for the smooth function $\alpha (\varphi )$. It is then shown that the models under consideration are compatible with the latest Planck 2018 constraints.

In this paper, we analyze the operation of an Otto cycle heat machine driven by a non-interacting two-dimensional electron gas on a twisted geometry. We show that due to both the energy quantization on this structure and the adiabatic transformation of the number of complete twists per unit length of a helicoid, the machine performance in terms of output work, efficiency, and operation mode can be altered. We consider the deformations as in a spring, which is either compressed or stretched from its resting position. The realization of classically inconceivable Otto machines, with an incompressible sample, can be realized as well. The energy-level spacing of the system is the quantity that is being either compressed or stretched. These features are due to the existence of an effective geometry-induced quantum potential which is of pure quantum-mechanical origin.

In this paper, we investigate the dynamical behavior of the universe with a flat FLRW model in $f(R,G)$ gravity, where $R$ and $G$ both signify the Ricci scalar and Gauss–Bonnet invariant. Furthermore, in order to determine the model’s behavior, it must have the late-time universe’s behavior, which involves both an accelerated expansion as well as ending in a big rip. We present a model that begins with a point-type singularity, i.e. a point with zero volume and infinite energy density, by using parametrization of the scale factor $a(t)$. The model’s actions are accelerating and expanding at the moment, and $\mathrm{\Lambda }$CDM in late times. Our extensive analysis encompasses the energy conditions, dynamics of certain model solutions and additional cosmological tests through a dominant model. Finally, the proposed framework acts exactly like a quintessence dark energy model in the current time and is reliable with standard cosmology $\mathrm{\Lambda }$CDM in late times.

By constructing models of quark stars (QSs), we use the MIT bag model as a strange quark matter equation of state (EoS). According to the strange matter hypothesis, the MIT bag model is the most successful phenomenological models of quarks confined to hadrons. This paper aims to explore the internal structure and the physical properties of QSs in the context of four-dimensional (4D) Einstein–Gauss–Bonnet (EGB) theory of gravity. The main feature of 4D EGB theory is that there is a nontrivial contribution to the gravitational dynamics in 4D spacetime. We present the essential features of QSs concerning the mass-radius relation depending on the interplay of matter parameters and the GB coupling constant. Our results show that all studied cases are found to be consistent with observations and physically relevant.

In this paper, we revisit the relation between the gradient-flow equations and Hamilton’s equations in information geometry. By regarding the gradient-flow equations as Huygens’ equations in geometric optics, we have related the gradient flows to the geodesic flows induced by the geodesic Hamiltonian in an appropriate Riemannian geometry. The original evolution parameter $t$ in the gradient-flow equations is related to the arc-length parameter in the associated Riemannian manifold by Jacobi–Maupertuis transformation. As a by-product, the relation between the gradient-flow equation and replicator equations is found.

We look into the cosmological uses of the new modified gravitational theory $\widehat{f}({𝒯},{{𝒯}}_G)$, which is based on the torsion invariant ${𝒯}$ and the teleparallel equivalent of the Gauss–Bonnet term ${{𝒯}}_G$. The corresponding cosmology of $\widehat{f}({𝒯},{{𝒯}}_G)$ gravity is very intriguing because it varies from both $f(T)$ theories and the $f(R,G)$ class of curvature-modified gravity. In this paper, we have investigated the applicability of an alternative gravitational theory called $\widehat{f}({𝒯},{{𝒯}}_G)$ by applying the energy conditions. Here, we assumed the form of $\widehat{f}(T,T_G)=-{𝒯}+\alpha ln\left[\right.{\beta }_1{({{𝒯}}^2+{\beta }_2{{𝒯}}_G)}^n\left]\right.$, where ${\beta }_1$ and ${\beta }_2$ are arbitrary constants. We have examined the cosmological applications of $\widehat{f}({𝒯},{{𝒯}}_G)$ gravity. Here, we consider two particular expressions of the time-dependent Hubble parameter. Both the model parameters are constrained jointly by the Observation Hubble dataset (OHD), the Pantheon dataset and the BAO data to constrain the model parameters using the Markov Chain Monte Carlo (MCMC) minimization technique. We determine the present values of Hubble constant for model $\zeta$: ${{\mathscr{H}}}_0=70_{-0.34}^{+0.34}$, $\zeta =1.2_{-0.016}^{+0.016}$ and ${{\mathscr{H}}}_0=1.8_{-0.013}^{+0.013}$; and model $A_2$: ${{\mathscr{H}}}_0=72_{-0.41}^{+0.41}$, $\zeta =1.5_{-0.0077}^{+0.0076}$ and $𝜖=1.3_{-0.012}^{+0.012}$ for the OHD+BAO+Pantheon dataset. Using the most recent estimated values of Hubble parameter, we properly analyzed the energy conditions and looked at the final behavior of our model. Additionally, we have explored the ${\omega }_D-{\omega }_D^{\prime }$ plane and also we have extracted the scalar field as well as potential of $\widehat{f}({𝒯},{{𝒯}}_G)$ gravity and its relationship to the tachyon field. In addition, we find that, depending on the model parameters, the dark energy (DE) equation-of-state (EoS) parameter may be quintessence or phantom-like, or it may undergo phantom-divide crossing. Finally, we find that all the essential features of the model are satisfied successfully.

Asymptotically Anti-de Sitter (AdS) Black Hole (BH) space–times are of theoretical and mathematical interest and attractive. On the other hand, in the last few decades, the theory of regular (nonsingular) BHs has gained many researchers and enthusiasts. Therefore, space–times asymptotically AdS and free of (essential) singularities can have a double attraction. An example of such space–time is the Regular Gaussian Black Hole (RGBH). In this paper, some thermodynamical properties of this BH are studied and examined through the calculation of thermodynamic functions and related diagrams. The results of the calculations and related diagrams indicate that a background AdS space–time is more compliant with the laws of the physical world than a de Sitter (dS) one. Finally, with a brief discussion about Geometrothermodynamics, it is clear that the space–time structure of RGBH supports the fundamental relationship between gravity, thermodynamics and quantum theory.

In this paper, we investigated anisotropic solution for a self-bound compact star model. The solution is obtained via Vaidya–Tikekar metric function $1/W(r)=\frac{K+C{r}^2}{K(1+C{r}^2)}$ and the vanishing complexity factor condition. The physical analysis of the solution has been discussed in detail which includes mass-radius ratio, and stability analysis via adiabatic index for a secondary component of the GW190814 event for different values $K$. Furthermore, we predicted the radii and obtained the compactness factor of different self-bound compact objects for different $K$. Moreover, the hydrostatic equilibrium condition of the solution is also checked. The physical result shows that the solution so obtained is well behaved and may be useful for modeling the self-bound compact objects as far as observational data is concerned.

The deformed Klein–Gordon equation has been solved in three-dimensional extended relativistic quantum mechanics (3D-ERQM) symmetries for the newly improved screened Kratzer potential (NISKP) model under the influence of the deformation space–space symmetries. The new relativistic energy eigenvalues were calculated using the parametric Bopp’s shift method and standard perturbation theory in addition to the approximation scheme suggested by Greene and Aldrich for the inverse square terms. The new relativistic energy eigenvalues of (LiH, HCl, CO and H₂) molecules under the NISKP model were shown to be sensitive to the atomic quantum numbers ($j,l,s,m$), mixed potential depths ($D_e,r_e$), the screening parameter’s inverse $(\alpha ,\delta )$, control parameter $\tau$ and non-commutativity parameters ($\mathrm{\Theta }$, $\beta$, $\zeta$). In addition, we analyzed the non-relativistic energy values by applying the well-known transmission rules known in the literature. Furthermore, we studied many special cases useful to researchers in the framework of the new extended symmetries, such as the new screened cosine Kratzer potential, the new screened Kratzer potential (SKP), the new Kratzer potential, the new coshine Yukawa potential, the new coshine Yukawa potential, the new shifted improved SKP and the new shifted SKP. The study is further extended to calculate the mass spectra of mesons of the heavy quarkonium system such as charmonium $c\overline{c}$, bottomonium $b\overline{b}$, $\overline{b}c$ and light mesons $c\overline{s}$ and $b\overline{s}$ that have the quark and antiquark flavor within the framework of the NISKP model in 3D-ENRQM symmetries.

This work deals with the investigation of several physical elements that contribute to the construction of stellar objects in the $f(R,G)$ theory, where $R$ and $G$ symbolize the Ricci and Gauss–Bonnet scalars, respectively. In the presence of an anisotropic source, we offer the fundamental formalization of this modified theory. To establish the physical viability of our models, we employ various methods. Energy conditions (ECs) will be derived to ensure the physical validity of our models within the context of $f(R,G)$ gravity. Moreover, we examine the physical viability through the assessment of radial and tangential sound speeds. Additionally, we analyze the equation of state (EoS) parameter and the anisotropic factor in the presence of the electromagnetic field’s influence. Dense stars are shown to be stable under anisotropy measures and exhibit their physical behavior under anisotropic stresses. We identify regions where the systems occupy high compactness and maintain stable ECs with a particular electric charge contribution.