International Journal of Geometric Methods in Modern Physics

In this paper, we present an introduction to cosmic inflation in the framework of Palatini gravity, which provides an intriguing alternative to the conventional metric formulation of gravity. In the latter, only the metric specifies the spacetime geometry, whereas in the former, the metric and the spacetime connection are independent variables—an option that can result in a gravity theory distinct from the metric one. In scenarios where the field(s) responsible for cosmic inflation are non-minimally coupled to gravity or the gravitational sector is extended, assumptions about the underlying gravitational degrees of freedom can have substantial implications for the observational effects of inflation. We examine this explicitly by discussing various compelling scenarios, such as Higgs inflation with a non-minimal coupling to gravity, Higgs inflation with a non-minimal derivative coupling, ${{ℛ}}^2$ inflation, and beyond. We also comment on reheating in these models. Finally, as an application of the general results of Palatini ${{ℛ}}^2$ inflation, we review a model of successful quintessential inflation, where a single scalar field acts initially as the inflaton and then becomes dynamical dark energy, in agreement will all experimental constraints.

This study is devoted to investigate the formation of compact stars using Tolman–Kuchowicz space-time in $f({𝒢},{𝒯})$ gravity. By taking into account the physically reliable formulations of metric potentials, $\xi$ = $B{r}^2+2\mathrm{\text{ln}}C$ and $\eta$ = $\mathrm{\text{ln}}(1+a{r}^2+b{r}^4)$, we investigate the equation of motion for spherically symmetric space-time in the presence of an anisotropic matter distribution. Furthermore, matching conditions are employed to compute the unknown constants. By making use of dynamical equations, the pivotal relevant aspects, including energy density, radial and tangential pressures, dynamical equilibrium, anisotropy effect, energy conditions and stability, are physically tested in order to determine the physical acceptability of yielding celestial model, which are thoroughly compared with experimental facts and figures of ten different compact stars. Finally, we observe that obtained anisotropic outcomes are physically viable, free from geometrical and physical singularities. Moreover, these outcomes also provide circumstantial evidence for the existence of super-massive compact stars.

There is an unavoidable association of traversability of wormholes to the violation of null energy condition which in turn indicates the presence of exotic or non-exotic matter in the wormhole geometry. The exotic matter possesses the negative energy that is required to sustain the wormhole. Recently studies are done to solve this problem so as to avoid the exotic matter. In this work, we attempt to find such solution in the framework of $F(R,T)$ gravity where $F(R,T)=R+2\lambda T$, here $R$ and $T$ are Ricci scalar and trace of energy momentum tensor respectively, using the Yukawa–Casimir shape function. For Yukawa–Casimir wormhole, it is assumed that the exotic energy is sourced from the Casimir energy density. We have examined the energy conditions using Yukawa–Casimir shape function

In this work, we study the autonomous dynamical system of different $F(R)$ models in the formalism of holographic dark energy using the generalized Nojiri–Odintsov cut-off. We explicitly give the expression of the fixed points as functions of the infrared cut-off for vacuum $F(R)$ gravity in flat and non-flat FRW background and for $F(R)$ coupling axion dark matter. Each fixed point component can be taken as a condition on the cut-off and on the expression of $F(R)$, leading to physically interesting constraints on these functions.

This paper attempts to study some geometric properties along with the existence of a generalized weakly Ricci symmetric manifold and find out the reduced form of defining conditions of such a manifold. It is observed that every generalized weakly Ricci symmetric manifold is an almost generalized pseudo-Ricci symmetric manifold. We also find out the conditions for which a weakly Ricci symmetric manifold becomes a Ricci pseudosymmetric manifold in the sense of Deszcz.

This work is devoted to study the behavior of massless particles within the context of curved spacetime. In essence, we investigate the consequences of the scale factor $C(\eta )$ of the Friedmann–Robertson–Walker metric in the Einstein–aether formalism to study photon-like particles. To do so, we consider the system within the canonical ensemble formalism in order to derive the following thermodynamic state quantities: spectral radiance, Helmholtz free energy, pressure, entropy, mean energy and the heat capacity. Moreover, the correction to the Stefan–Boltzmann law and the equation of states are also provided. Particularly, we separate our study within three distinct cases, i.e. $s=0,$ $p=0$; $s=1,$ $p=1$; $s=2,$ $p=1$. In the first one, the results are derived numerically. Nevertheless, for the rest of the cases, all the calculations are accomplished analytically showing explicitly the dependence of the scale factor $C(\eta )$ and the Riemann zeta function $\xi (s)$. Furthermore, our analyses are accomplished in general taking into account three different regimes of temperature of the universe, i.e. the inflationary era ($T=10^{13}$GeV), the electroweak epoch ($T=10^3$GeV) and the cosmic microwave background ($T=10^{-13}$GeV).

In this paper, we discuss the fields described by Dirac wave equation written in Clifford algebra based on Macfalane quaternions. It is shown that the strengths of these fields are nonzero only in the area of sources and the interaction of such fields occurs by overlapping. We consider both the simple spherically symmetric models of sources, which demonstrate attractive and repulsive interaction, and more complicated core-shell systems, which provide the bound states formation.

First, we illustrate that a Ricci symmetric quasi-Einstein spacetime is a static spacetime and belongs to Petrov classification $I$, $D$ or $O$. We investigate conformally flat quasi-Einstein spacetime as a solution of $f({ℛ},G)$-gravity theory and explain the physical meaning of the Friedmann–Robertson–Walker metric. For the models $f({ℛ},G)=\mu {{ℛ}}^{{\beta }_1}{G}^{{\beta }_2}$, (${\beta }_1$, ${\beta }_2$ and $\mu$ are constants) and $f({ℛ},G)={{ℛ}}^2-6G$, various energy conditions in terms of associated scalars are examined. These models satisfy the weak, null, and dominant energy conditions, while violating the strong energy condition, which is in good agreement with recent empirical investigations that show the Universe is currently in an accelerating phase.

In this paper, we construct a surface family possessing a Mannheim B-pair of a given curve as an asymptotic curve. Using the Bishop frame of the given Mannheim B curves, we present the surface as a linear combination of this frame and analyze the necessary and sufficient condition for a given curve such that its Mannheim B-pairs are both isoparametric and asymptotic on a parametric surface. The extension to ruled surfaces is also outlined. In addition, necessary and sufficient conditions have been given for the development of this ruled surface family. Finally, we present some interesting examples to show the validity of this study.

The main purpose of this research is to examine a number of interior configurations of stable anisotropic objects formed in the shape of spherical charged stars within the gravity region described by $f(R,G)$, where $G$ represents the Gauss–Bonnet invariant and $R$ defines the Ricci Scalar in this scenario. The formation of these charged stars is investigated using the solutions found by Karori and Barua, among several feasible models within the theory of $f(R,G)$ gravity. The study explores the behavior of these realistically charged compact stars, analyzing various physical components through the use of graphs. Furthermore, the feasibility of our model is assessed by evaluating it against different energy conditions. Additionally, topics such as density modification, stress evolution, various forces, star stability, anisotropy measurement, state parameter equations, and charge distribution are discussed.

The generalized momentum operators are derived in the framework of non-relativistic quantum mechanics, taking into account an especial assumption on the covariant derivative. According to this assumption, a scalar density doesn’t change under the action of covariant derivative. The Hermitian form of the covariant derivative is discussed. It is shown that, with the help of the adjoint of covariant derivatives, generalized momentum operators can be derived. The inverse of covariant derivative is calculated. It is shown that the inverse of generalized momentum operators can be deduced from the inverse of covariant derivatives.

The electrodynamics of the highly magnetized and spherical symmetric neutron star within the framework of special relativity has been investigated. It is assumed that the neutron star is isolated and consists of highly conducting matter. Explicit demonstrations were made regarding the multipole solutions for both axially symmetric and non-axially symmetric electromagnetic fields surrounding the neutron star. It was observed that the axially symmetric solutions are independent of time, whereas the non-axially symmetric solutions are time-dependent. Additionally, wave-like solutions for the electromagnetic field in TE and TM modes were derived.

The current analysis uses the non-static plane symmetric space-time to dynamically examine the holographic dark energy model as candidates of IR cut-offs (specifically Hubble’s and Granda–Oliveros cut-off). Any other cut-off is just a specific example of the Nojiri–Odintsov cut-off, which is the most universal [S. Nojiri and S. D. Odintsov, Gen. Relativity Gravitation 38 (2006) 1285]. Using the Markov Chain Monte Carlo (MCMC) method, we estimate the best fit values for the model parameters imposed from the combined datasets of CC+SC+BAO. Now, it has been found that the characteristics of space-time that have been addressed and formulated using both models are flat universe and observed that the model appears to be in good agreement with the observations. In addition, we investigate the behavior of equation of state (EoS) parameters along with the energy conditions. Finally, we found that in both the cut-offs the models predict that the present and late universe are accelerating and the EoS parameter behaves like the quintessence model.

We show that the ideas related to integrability and symmetry play an important role not only in the string T-duality story but also in its point particle counterpart. Applying those ideas, we find that the T-duality seems to be a more widespread phenomenon in the context of the point particle dynamics than it is in the string one; moreover, it concerns physically very relevant point particle dynamical systems and not just somewhat exotic ones fabricated for the purpose. As a source of T-duality examples, we consider maximally superintegrable spherically symmetric electro-gravitational backgrounds in $n$ dimensions. We then describe in detail four such spherically symmetric dynamical systems which are all mutually interconnected by a web of point particle T-dualities. In particular, the dynamics of a charged particle scattered by a repulsive Coulomb potential in a flat space is T-dual to the dynamics of the Coulomb scattering in the space of constant negative curvature, but it is also T-dual to the (conformal) Calogero–Moser inverse square dynamics both in flat and hyperbolic spaces. Thus knowing just the Hamiltonian dynamics of the scattered particle cannot give us information about the curvature of the space in which the particle moves.

This paper aims to reveal the effects of the fourth-order dispersion and parabolic law which comes from self-phase modulation on the soliton behavior of the cubic-quartic nonlinear Schrödinger equation (CQ-NLSE) by using the modified new Kudryashov method. First, applying the complex wave transformation, the nonlinear ordinary differential form (NODE) has been obtained. Then, the modified new Kudryashov method (mNKM) has been expressed and applied. In the next step, linear algebraic system has been gained and solved. Then analytical soliton solution of the CQ-NLSE has been derived and checked for accuracy so that it satisfies the main equation. For the obtained solution functions, bright and singular soliton solutions have been gained and their graphical presentations have been made. The effects of both the fourth-order dispersion parameter and the parabolic law nonlinearity on the soliton dynamics have been examined and the necessary comments have been made. To our best knowledge, no such study has been reported for the equation examined.

The tunnel-like structures proposed by Morris and Thorne are explored in this study by using $f({ℛ},{𝒯})$ framework. The solutions of static wormhole, supported by the matter possess van der Waals equation of state, are derived by two possible schemes. We have explored the shape function and energy conditions including null, weak, strong and dominant conditions. For this purpose, we used the equation of state $p_r=-\alpha {\rho }^2$ in first scheme and a numerical technique in second scheme. Also, the radius of the wormhole’s throat is calculated, within which the energy conditions are satisfied. We have also deliberated the graphical illustrations of all the solutions.

We discuss generalizations of the notions of projective transformations acting on affine model of Riemann–Cartan and Riemann–Cartan–Weyl gravity which preserve the projective structure of the light-cones. We show how the invariance under some projective transformations can be used to recast a Riemann–Cartan–Weyl geometry either as a model in which the role of the Weyl gauge potential is played by the torsion vector, which we call torsion-gauging, or as a model with traditional Weyl (conformal) invariance.

In this work, formal theoretical aspects concerning conformally invariant functional actions of electrodynamics are presented and discussed. In particular, the origin of the conformal and duality invariant Lagrangians of [I. Bandos et al., J. High Energy Phys. 10 (2021) 031; I. Bandos, K. Lechner, D. Sorokin and P. Townsend, Phys. Rev. D 102 (2020) 121703] (e.g. ModMax) and also Born–Infeld types are analyzed being its non-abelian counterpart presented and discussed explicitly for the gauge group SU(2). Implications on the properties of the gravitational field are briefly discussed by means of new symmetries of the field equations.