Related papers: Noether symmetries in Bianchi universes
The exact solutions of spherically symmetric space-times are explored by using Noether symmetries in $f(R,\phi,X)$ gravity with $R$ the scalar curvature, $\phi$ a scalar field and $X$ the kinetic term of $\phi$. Some of these solutions can…
Centre manifold theory is applied to some dynamical systems arising from spatially homogeneous cosmological models. Detailed information is obtained concerning the late-time behaviour of solutions of the Einstein equations of Bianchi type…
We derive the Lie and the Noether conditions for the equations of motion of a dynamical system in a $n-$dimensional Riemannian space. We solve these conditions in the sense that we express the symmetry generating vectors in terms of the…
The phase space of Bianchi I universes in vacuum Brans-Dicke gravity is analyzed in terms of physical variables. The behaviour of the solutions of the field equations near the fixed points (which are solutions of Einstein gravity) is…
We investigate the evolution of anisotropies in Bianchi I spacetimes within the framework of the 4D Einstein-Gauss-Bonnet scalar field theory. The field equations are formulated using dimensionless variables, and the asymptotic dynamics are…
By employing the Bianchi identities for the Riemann tensor in conjunction with the Einstein equations, we construct a first order symmetric hyperbolic system for the evolution part of the Cauchy problem of general relativity. In this…
Self-consistent solutions to nonlinear spinor field equations in General Relativity have been studied for the case of Bianchi type-I space-time filled with perfect fluid. The initial and the asymptotic behavior of the field functions and…
A self-consistent system of interacting nonlinear spinor and scalar fields within the scope of a Bianchi type-I cosmological model filled with perfect fluid is considered. Exact self-consistent solutions to the corresponding field equations…
In this work we construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus. The corresponding action in four dimensions is similar to…
For the non-tachyonic curvature squared action we show that the expanding Bianchi-type I models tend to the dust-filled Einstein-de Sitter model for t tending to infinity if the metric is averaged over the typical oscillation period.…
We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on…
In this paper we investigate a Bianchi type I transitioning Universe in Brans-Dicke theory. To get an explicit solution of the field equations, we assume scalar field as $\phi = \phi_{0}\left[t^{\alpha}exp(\beta t)\right]^{\delta}$ with…
As it is well known, symmetry plays a crucial role in the theoretical physics. On other hand, the Noether symmetry is a useful procedure to select models motivated at a fundamental level, and to discover the exact solution to the given…
We develop the $n$-dimensional cosmology for $f(\mathcal{G})$ gravity, where $\mathcal{G}$ is the \emph{Gauss-Bonnet} topological invariant. Specifically, by the so-called Noether Symmetry Approach, we select $f(\mathcal{G})\simeq…
We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on…
We study the Lie point symmetries of Einstein's equations for the Friedmann-Roberstson-Walker Cosmology. They form either a two - dimensional or a three - dimensional solvable group depending on the form of the self interacting potential.…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
We discuss non-minimally coupled cosmologies involving different geometric invariants. Specifically, actions containing a non-minimally coupled scalar field to gravity described, in turn, by curvature, torsion and Gauss--Bonnet scalars are…
This article deals with the study of Bianchi type-I universe in the context of f(R,T) gravity. Einstein's field equations in f(R,T) gravity has been solved in presence of cosmological constant ? and quadratic equation of state. Here we have…
This manuscript is devoted to investigate Bianchi Type $I$ universe in the context of $f(R,T)$ gravity. For this purpose, we explore the exact solutions of locally rotationally symmetric Bianchi type $I$ spacetime. The modified field…