Narrow Results

This paper deals with the confinement mechanism of chiral fermions evolving in a five-dimensional spacetime, with S³ × R four-dimensional slices. To construct the proper Yukawa-type Lagrangian, we must solve the Gordon and Dirac-type equations in the bulk. An intriguing fact that emerges from our analysis is that only the left-handed fermions can be trapped on the brane. Characterizing the wave functions by the quantum number m_ℓ, it turns out that for m_ℓ = 3/2 and m_ℓ ∈ {0, ±1}, once the coupling constant increases, the left-handed modes become more and more dominant in the brane, away from the {z = 0}-singularity.

This paper investigates the existence and stability of Einstein universe in the context of f(R, T, Q) gravity, where Q = R${}_{\mu \nu }$T${}^{\mu \nu }$. Considering linear homogeneous perturbations around scale factor and energy density, we formulate static as well as perturbed field equations. We parametrize the stability regions corresponding to conserved as well as non-conserved energy–momentum tensor using linear equation of state parameter for particular models of this gravity. The graphical analysis concludes that for a suitable choice of parameters, stable regions of the Einstein universe are obtained which indicates that the big bang singularity can be avoided successfully by the emergent mechanism in non-minimal matter-curvature coupled gravity.

The aim of this paper is to investigate the existence of stable modes of the Einstein static universe in the background of $f(R)$ theory. For this purpose, we take homogeneous anisotropic perturbations in scale factors as well as matter contents. We construct static and perturbed field equations that are further parameterized by linear equation of state parameter. We obtain the Einstein static solutions for two specific $f(R)$ models and graphically analyze their stable regions. It is concluded that contrary to general relativity, there exists stable Einstein static universe with anisotropic perturbations.

The aim of this paper is to investigate the stability of Einstein static cosmos using anisotropic homogeneous perturbations in the background of $f(R,T)$ theory in which $R$ and $T$ express the Ricci scalar and trace of the stress–energy tensor, respectively. To accomplish this work, we consider perfect fluid distribution and adopt small anisotropic perturbations in the scale factors and matter contents. We develop static and perturbed field equations that are simplified by using equation of state parameter. For the specific models of $f(R,T)$ theory with conserved and non-conserved stress–energy tensor, the Einstein solutions are explored and their stability regions are analyzed graphically. We conclude that the static Einstein stable universe with anisotropic perturbations exists in this framework contrary to general relativity.

We study UV-finite theory of induced gravity. We use scalar fields, Dirac fields and vector fields as matter fields whose one-loop effects induce the gravitational action. To obtain the mass spectrum that satisfies the UV-finiteness condition, we use a graph-based construction of mass matrices. The existence of a self-consistent static solution for an Einstein universe is shown in the presence of degenerate fermions.

We consider the Casimir effect, by calculating the Casimir energy and its corrections for nonzero temperatures, of a massless scalar field in the spacetime with topology $S^3\times R^1$ (Einstein universe) containing an idealized cosmic string. The obtained results confirm the role played by the identifications imposed on the quantum field by boundary conditions arising from the topology of the gravitational field under consideration and illustrate a realization of a gravitational analogue of the Casimir effect. In this backgorund, we show that the vacuum energy can be written as a term which corresponds to the vacuum energy of the massless scalar field in the Einstein universe added by another term that formally corresponds to the vacuum energy of the electromagnetic field in the Einstein universe, multiplied by a parameter associated with the presence of the cosmic string, namely, $\lambda =(1/\alpha )-1$, where $\alpha$ is a constant related to the cosmic string tension, $G\mu$.

This paper explores the stability of the Einstein universe against linear homogeneous perturbations in the background of $f({𝒢},T)$ gravity. We construct static as well as perturbed field equations and investigate stability regions for the specific forms of generic function $f({𝒢},T)$ corresponding to conserved as well as nonconserved energy-momentum tensor. We use the equation-of-state parameter to parameterize the stability regions. The graphical analysis shows that the suitable choice of parameters lead to stable regions of the Einstein universe.

We investigate the existence and stability of the Einstein universe in the context of f (R, T, Q) gravity, where Q = R_μνT^μν. Considering linear homogeneous perturbations around scale factor and energy density, we formulate static as well as perturbed field equations. We parameterize the stability regions corresponding to conserved as well as non-conserved energy-momentum tensor using linear equation of state parameter for particular models of this gravity. The graphical analysis concludes that for a suitable choice of parameters, the stable regions of the Einstein universe are obtained which indicate that the big-bang singularity can be avoided successfully by the emergent mechanism in non-minimal matter-curvature coupled gravity.

Flat Lorentz (3, 1) space is the natural home for Einstein's Special Theory of Relativity, with three "space" dimensions and one "time" dimension. The geometry naturally encodes the ideas of inertial frames, time and space dilation. Much of the mathematical terminology and research interests are infused with physical considerations, but purely mathematical questions are at the core of this treatment.

This is an introduction to Lorentzian (n, 1) geometry for all n ≥ 1, examining the constant curvature spaces: flat, de Sitter (positive curvature) and anti-de Sittter spaces. The conformal boundaries of these Lorentz spacetimes will also be constructed. The connection between Lorentz (2, 1) geometry and geometry of the hyperbolic plane will also be investigated.

Historically the earliest general relativistic cosmological solution was received by Einstein himself as homogenous, isotropic one. In accordance with European cosmology it was expected static. The Eternal Universe as scientific model is conflicting with the existed theological model of the Universe created by God, therefore, of the limited age. Christianity, younger Islam, older Judaism are based on creationism. Much older oriental traditions such us Hinduism and Buddhism are based on conceptions of eternal and cyclic Universe which are closer to scientific worldview. To have static universe Einstein needed a factor to counteract gravity and postulated cosmological term and considered it as a disadvantage of the theory. This aesthetic dissatisfaction was amplified by interpretation distance-redshift relationship as a cosmological expansion effect. Emerged scientific cosmological community (excluding Hubble himself – almost always) endorsed the concept of expanding Universe. At the same time, as it is shown in this report, a natural well known factors do exist to counteract gravity. They are inertial centrifugal and Coriolis forces finding their geometrical presentation in the relativity theory.