In this work, we are investigating the problem of integrability of Bianchi class A cosmological models. This class of systems is reduced to the form of Hamiltonian systems with exponential potential forms. The dynamics of Bianchi class A models is investigated through the EulerLagrange equations and geodesic equations in the Jacobi metric. On this basis, we have come to some general conclusions...

In the second self-creation theory of gravitation and in the general theory of relativity, Bianchi type VI0 cosmological model in the presence of viscous fluid is studied. An exact solution of the field equations is given by considering the cosmological model yields a constant decelerations parameter q=constant and the coefficients of the metric are taken as A(t)=[c1t+c<su...

We investigate the effect of dark energy on the limits on the shear anisotropy in spatially homogeneous Bianchi cosmological models obtained from measurements of the temperature anisotropies in the cosmic microwave background. We shall primarily assume that the dark energy is modelled by a cosmological constant. In general, we find that there are tighter bounds on the shear than in models with ...

EYL [1] first try to unify gravitation and electromagnetism in single space-time geometry. He showed how one can introduce vector field in the Riemannian space time with an intrinsic geometric significance, but this theory was not accepted. Later Lyra’s [2] proposed a modification of Riemannian geometry by introducing a gauge function into the structureless manifold that bears close resemblance...

The dynamics of the Einstein-Vlasov equations for a class of cosmological models with four Killing vectors is discussed in the case of massive particles. It is shown that in all models analysed the solutions with massive particles are asymptotic to solutions with massless particles at early times. It is also shown that in Bianchi types I and II the solutions with massive particles are asymptoti...

A convenient framework is developed to generalize Berry’s investigation of the adiabatic geometrical phase for a classical relativistic charged scalar field in a curved background spacetime which is minimally coupled to electromagnetism and an arbitrary (non-electromagnetic) scalar potential. The general formalism which is applicable for any scalar field equation which involves time derivatives...

We complete the study of the analytic integrability of the Class A of Bianchi cosmological models with k = 1, characterizing the analytic first integrals of the Bianchi types VI0 and VIII0.