We undertake a detailed analysis of the symmetry structures of the plane symmetric and the locally rotationally symmetric (LRS) Bianchi type I spacetimes in the [Formula: see text] gravity. In particular, we construct all the variational symmetries associated with its Lagrangian and, in some cases, construct the associated conservation laws using Noether’s theorem. Giving a comparison between isometries and variational symmetries, we give symmetry structures of some well-known spacetimes.
We show that one can find a useful compactified representation of minisuperspace dynamics using conformal diagrams and how global and asymptotic qualitative features of the dynamics can be inferred from. the diagrams. To provide explicit examples this is done for the locally rotationally symmetric Bianchi type I and IX models.
In this paper, we investigate locally rotationally symmetric (LRS) Bianchi type-I cosmological model containing stiff matter with a cosmological term proportional to the Hubble parameter. This variation law for vacuum density has recently been proposed by Schützhold on the basis of quantum field estimations in the curved and expanding background. The model obtained approaches isotropy. The cosmological term tends asymptotically to a genuine cosmological constant and the model tends to a de Sitter universe. We obtain that the present universe is accelerating with a large fraction of cosmological density in the form of cosmological term. Taking matter density equal to half of the vacuum density, as suggested by observation, we obtain a universe age given by Ht = 0.55 and a decelerating parameter equal to 2σ2/3H2.
We study the locally rotational symmetry Bianchi type-I dark energy model in the framework of f(T) theory of gravity, where T denotes the torsion scalar. A viable cosmological model is undertaken and the isotropization of this latter is checked, yielding a result that reflects the real evolution of our universe. Moreover, still in the anisotropic optic, a more complicated f(T) model is obtained from the cosmological reconstruction scheme and the analysis shows that the universe is more anisotropic at the beginning if the terms of higher order in T are not considered. This means that the nonlinear model should be favored by observational data.
Locally Rotationally Symmetric Bianchi Type-I Cosmological Model in f(R,T) Gravity
