Related papers: Superspace and global stability in General Relativ…
The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the…
The generalized covariant derivative on 5-dimen-sional space including 1-dimensional extra compact space is defined, and, by use of it, the Weinberg-Salam model is reconstructed. The spontaneous breakdown of symmetry takes place owing to…
The canonical structure of supergravity with a cosmological constant is analyzed in 2 + 1 dimensions using the Dirac constraint formalism. The first class constraints are used to find two Bosonic and one Fermionic gauge symmetries that…
If spacetime possesses extra dimensions of size and curvature radii much larger than the Planck or string scales, the dynamics of these extra dimensions should be governed by classical general relativity. We argue that in general…
The bigravity models coupled with two scalar fields are constructed. We show that a wide class of the expansion history of the universe, especially corresponding to dark energy and/or inflation, can be described by a solution of the…
A brief introduction on the issue of stability in generalized modified gravity is presented and the dynamical system methods are used in the investigation of the stability of spatially flat homogeneous cosmologies within a large class of…
This paper proves the stability, with respect to the evolution determined by the vacuum Einstein equations, of the Cartesian product of high-dimensional Minkowski space with a compact, Ricci-flat Riemannian manifold that admits a spin…
We investigate the presence of defect structures in generalized models described by real scalar field in $(1,1)$ space-time dimensions. We work with two distinct generalizations, one in the form of a product of functions of the field and…
The stability criteria for the generalized Brans-Dicke cosmology in a spatially flat, homogeneous and isotropic cosmological model is discussed in the presence of a perfect fluid. The generalization comes through the channel that the…
In this paper the four-dimensional space-velocity Cosmological General Relativity of Carmeli is developed by a general solution to the Einstein field equations. The metric is given in the Tolman form and the vacuum mass density is included…
We study a class of dynamical systems for which the motions can be described in terms of geodesics on a manifold (ordinary potential models can be cast into this form by means of a conformal map). It is rigorously proven that the geodesic…
We investigate the modified gravity theories in terms of the effective dark energy models. We compare the cosmic expansion history and the linear growth in different models. We also study the evolution of linear cosmological perturbations…
Assuming that Quantum Mechanics is universal and that it can be applied over all scales, then the Universe is allowed to be in a quantum superposition of states, where each of them can correspond to a different space-time geometry. How can…
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…
Minisuperpace Quantum Cosmology is an approach by which it is possible to infer initial conditions for dynamical systems which can suitably represent observable and non-observable universes. Here we discuss theories of gravity which, from…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…
It has long been considered that conformal superspace is the natural configuration space for canonical general relativity. However, this was never definitively demonstrated. We have found that the standard conformal method of solving the…
The theory presented in this monograph establishes the first mathematically rigorous result on the global nonlinear stability of self-gravitating matter under small perturbations of an asymptotically flat, spacelike hypersurface of…
It is useful to study the space of all cosmological models from a dynamical systems perspective, that is, by formulating the Einstein field equations as a dynamical system using appropriately normalized variables. We will discuss various…
Global stability of the systems has always been vital of importance; however, this concept has not yet been sufficiently developed for the nonlinear systems. This paper extends the Jacobian matrix so that this method be able to seek the…