International Journal of Geometric Methods in Modern Physics

In this paper, we first correct a recent misconception about a topology that was suggested by Zeeman as a possible alternative to his fine topology. This misconception appeared while trying to establish the causality in the ambient boundary-ambient space cosmological model. We then show that this topology is actually the intersection topology (in the sense of Reed [The intersection topology w.r.t. the real line and the countable ordinals, Trans. Am. Math. Soc. 297(2) (1986) 509–520]) between the Euclidean topology on ${ℝ}^4$ and the order topology whose order, namely horismos, is defined on the light cone and we show that the order topology from horismos belongs to the class of Zeeman topologies. These results accelerate the need for a deeper and more systematic study of the global topological properties of spacetime manifolds.

This work provides some feasible regions for the existence of traversable wormhole geometries in modified $f({𝒢},T)$ gravity. For this purpose, three different matter contents have been studied with special emphasis on anisotropic fluid by considering a specific $f({𝒢},T)$ gravity power law model. It has been shown that the null energy conditions for the effective energy–momentum tensor are widely violated for the ordinary matter content. However, some small feasible regions to support the wormhole solutions have been noted. Furthermore, the stability of the anisotropic feasible regions for the wormhole solutions has been discussed. It is concluded that the wormhole geometries threaded by the ordinary matter actually exist and are well stable in $f({𝒢},T)$ gravity.

In this work, we use the Loop Quantum Cosmology (LQC) modified scalar–tensor reconstruction techniques in order to investigate how bouncing and inflationary cosmologies can be realized. With regard to the inflationary cosmologies, we shall be interested in realizing the intermediate inflation and the Type IV singular inflation, while with regard to bouncing cosmologies, we shall realize the superbounce and the symmetric bounce. In all the cases, we shall find the kinetic term of the LQC holonomy corrected scalar–tensor theory and the corresponding scalar potential. In addition, we shall include a study of the effective Equation of State (EoS), emphasizing at the early- and late-time eras. As we demonstrate, in some cases it is possible to have a nearly de Sitter EoS at the late-time era, a result that could be interpreted as the description of a late-time acceleration era. Also, in all cases we shall examine the dynamical stability of the LQC holonomy corrected scalar-tensor theory, and we shall confront the results with those coming from the corresponding classical dynamical stability theory. The most appealing cosmological scenario is that of a Type IV singular inflationary scenario, in which the singularity may occur at the late-time era. As we demonstrate, for this model, during the dark energy era, a transition from non-phantom to a phantom dark energy era occurs.

We consider the $𝔞𝔣𝔣(1|1)$-module structure on the spaces of differential operators acting on the spaces of weighted densities. We compute the second differential cohomology of the Lie superalgebra $𝔞𝔣𝔣(1|1)$ with coefficients in differential operators acting on the spaces of weighted densities. We classify formal deformations of the $𝔞𝔣𝔣(1|1)$-module structure on the superspaces of symbols of differential operators. We prove that any formal deformation of a given infinitesimal deformation of this structure is equivalent to its infinitesimal part. This work is the simplest superization of a result by Basdouri [Deformation of $𝔞𝔣𝔣(1)$-modules of pseudo-differential operators and symbols, J. Pseudo-differ. Oper. Appl. 7(2) (2016) 157–179] and application of work by Basdouri et al. [First cohomology of $𝔞𝔣𝔣(1)$ and $𝔞𝔣𝔣(1|1)$ acting on linear differential operators, Int. J. Geom. Methods Mod. Phys. 13(1) (2016)].

Here, the scalar curvature of an Einstein-type manifold or equivalently an almost Yamabe quasi-soliton is explicitly determined in terms of its soliton function and some rigidity theorems are obtained. Among the others its shown; if the soliton function is negative, then every compact conformal Yamabe quasi-soliton is isometric to the standard Euclidean sphere.

A hom-Lie algebroid is a vector bundle together with a Lie algebroid like structure which is twisted by a homomorphism. In this paper, we use the idea of representations up to homotopy of Lie algebroids to construct a same structure for hom-Lie algebroids and we will explain how representations up to homotopy of length 1 are related to extensions of hom-Lie algebroids.

In this paper, we investigate homothetic Ricci collineations (HRCs) for non-static plane symmetric spacetimes. The source of the energy–momentum tensor is assumed to be a perfect fluid. Both degenerate as well as non-degenerate cases are considered and the HRC equations are solved in different cases. It is concluded that these spacetimes may possess 6, 7, 8, 10 or 11 HRCs in non-degenerate case, while they admit seven or infinite number of HRCs for degenerate Ricci tensor.

A class of spatially homogeneous and anisotropic Bianchi-V massive string models have been studied in the modified $f(R,T)$-theory of gravity proposed by Harko et al. [Phys. Rev. D 84:024020, 2011] in the presence of magnetic field. For a specific choice of $f(R,T)=f_1(R)+f_2(T)$, where $f_1(R)={\nu }_{1}R$ and $f_2(T)={\nu }_{2}T$; ${\nu }_1$, ${\nu }_2$ being arbitrary parameters, solutions of modified gravity field equations have been generated. To find the deterministic solution of the field equations, we have considered the time varying deceleration parameter which is consistent with observational data of standard cosmology (SNIa, BAO and CMB). As a result to study the transit behavior of Universe, we consider a law of variation for the specifically chosen scale factor, which yields a time-dependent deceleration parameter comprising a class of models that depicts a transition of the Universe from the early decelerated phase to the recent accelerating phase. In this context, for the model of the Universe, the field equations are solved and corresponding cosmological aspects have been discussed. The Energy conditions in this modified gravity theory are also studied. Stability analysis of the solutions through cosmological perturbation is performed and it is concluded that the expanding solution is stable against the perturbation with respect to anisotropic spatial direction. Some physical and geometric properties of the models are also discussed.

We classify deformations of $𝔬𝔰𝔭(2|2)$-module structure on the space ${𝔖}_d^2={\oplus }_{k=0}^{\infty }{𝔉}_{d-\frac{k}{2}}^2$, where ${𝔉}_{\lambda }^2$ is the space of $\lambda$-densities on ${ℝ}^{1|2}$.

A generalized dynamical equation for the scale factor of the universe is proposed to describe the cosmological evolution by considering the bulk viscosity $\zeta$ and time dependent parameter $\mathrm{\Lambda }$ as linear combination of two terms of the form $\zeta ={\zeta }_0+{\zeta }_{1}H$ and $\mathrm{\Lambda }(t)={\mathrm{\Lambda }}_0+{\mathrm{\Lambda }}_{1}H,$ i.e. one is constant and other is proportional to the scalar expansion $𝜃=3\frac{ȧ}{a}.$ In this framework, we obtained the analytical solution of the field equations for the scale factor $a(t),$ scalar field potential $V(\phi )$ with effective equation of state (EoS) of the form $p=\omega (\rho )\rho +\mathrm{\Lambda }(t),$ where $\omega (\rho )=A_0{\rho }^{\alpha -1}-1$. The final results are compared with previously known results for the model with scalar field.

In this paper, we introduce the concept of periodic Gabor frames on non-Archimedean fields of positive characteristic. We first establish a necessary and sufficient condition for a periodic Gabor system to be a Gabor frame for $L^2(\mathrm{\Omega })$. Then, we present some equivalent characterizations of Parseval Gabor frames on non-Archimedean fields by means of some fundamental equations in the time domain. Finally, potential applications of Gabor frames on non-Archimedean fields are also discussed.

In this paper, we consider a pseudo-Riemannian manifold equipped with a Kähler–Norden–Codazzi golden structure. For such a manifold, we study curvature properties. Also, we define special connections of the first type and of the second type on the manifold, which preserve the associated twin Norden golden metric and satisfy some special conditions and present some results concerning them.

Given a compact Riemann surface $X$ and a moduli space $M_{\alpha }(\mathrm{\Lambda })$ of parabolic stable bundles on it of fixed determinant of complete parabolic flags, we prove that the Poincaré parabolic bundle on $X\times M_{\alpha }(\mathrm{\Lambda })$ is parabolic stable with respect to a natural polarization on $X\times M_{\alpha }(\mathrm{\Lambda })$.

We apply the Wick rotation to the Monge–Ampère equation of Tzitzeica graphs and we introduce the Wick–Tzitzeica solitons as complex functions solving the new equation. Some known Tzitzeica surfaces yields examples of these new solitons and we analyze them. To a second Wick–Tzitzeica soliton, we associate a homogeneous ODE system of gradient type which is Nambu–Poisson.

We study the Einstein static universe (ESU) in the framework of Generalized Uncertainty Principle (GUP) constructed by the Snyder non-commutative space. It is shown that the deformation parameter can induce an effective energy density subject to GUP which obeys the holographic principle (HP) and plays the role of a cosmological constant. Using the holographic feature of this effective energy density, we introduce natural IR and UV cut-offs which depend on the GUP-based effective equation of state. Moreover, we propose a solution to the cosmological constant problem (CCP). This solution is based on the result that the Einstein equations just couple to the tiny holographic-based surface energy density (cosmological constant) induced by the deformation parameter, rather than the large quantum gravitational-based volume energy density (vacuum energy) having contributions of order $M_P^4$.

We study different manifestations of the speed of light in theories of gravity where metric and connection are regarded as independent fields. We find that for a generic gravity theory in a frame with locally vanishing affine connection, the usual degeneracy between different manifestations of the speed of light is broken. In particular, the space-time causal structure constant ($c_{\mathrm{\text{ST}}}$) may become variable in that local frame. For theories of the form $f({ℛ},{{ℛ}}^{\mu \nu }{{ℛ}}_{\mu \nu })$, this variation in $c_{\mathrm{\text{ST}}}$ has an impact on the definition of the luminosity distance (and distance modulus), which can be used to confront the predictions of particular models against Supernovae type Ia (SN Ia) data. We carry out this test for a quadratic gravity model without cosmological constant assuming (i) a constant speed of light and (ii) a varying speed of light (VSL), and find that the latter scenario is favored by the data.

We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a $(2+1)$-dimensional Riemann (curved) spacetime. Nonequivalent complete sets of mutually commuting symmetry operators are classified in a $(2+1)$-dimensional Minkowski (flat) space. For each of the sets, we carry out a complete separation of variables in the Dirac equation and find a corresponding electromagnetic potential permitting separation of variables.

We present an explicit analytical computation of the quantum corrections, at next-to-leading order, to the critical exponents. We employ for that the Unconventional minimal subtraction, recently proposed, and the Callan–Symanzik methods to probe the universality hypothesis by comparing the outcomes for the critical exponents evaluated in both methods and the ones calculated previously in massless theories renormalized at different renormalization schemes. Furthermore, the consistency of the former method is investigated for the first time in literature, to our knowledge. At the end, we compute the critical exponents at any loop level by an induction process and furnish the physical interpretation of the results.