We consider conformally invariant form of the actions in Einstein, Weyl, Einstein-Cartan and Einstein-Cartan-Weyl space in general dimensions(> 2) and investigate the relations among them. In Weyl space, the observational consistency condition for the vector field determining non-metricity of the connection can be obtained from the equation of motion. In Einstein-Cartan space a similar role is played by the vector part of the torsion tensor. We consider the case where the trace part of the torsion is the Kalb-Ramond type of field. In this case, we express conformally invariant action in terms of two scalar fields of conformal weight −1, which can be cast into some interesting form. We discuss some applications of the result.

We consider a cosmology with a noncompact nonlinear sigma model. The target space is of de Sitter type and four scalar fields are introduced. The potential is absent but cosmological constant term Λ is added. One of the scalar fields is time dependent and the remaining three fields have no time dependence but only spatial dependence. We show that a very simple ansatz for the scalar fields results in the accelerating universe with an exponential expansion at late times. It is pointed out that the presence of the energy density and pressure coming from the spatial variation of the three scalar fields plays an essential role in our analysis which includes Λ = 0 as a special case and it discriminate from the standard Λ-dominated acceleration. We perform a stability analysis of the solutions and find that some solutions are classically stable and attractor. We also present a nonperturbative solution which asymptotically approaches an exponential acceleration and discuss possible cosmological implications in relation to dark energy. It turns out that the equation of state approaches asymptotically ω = −1 both from above and below, but the crossing does not occur. It predicts present value of ω ∼ −1 ∓ 0.07, which is within the region allowed by the observational data. This solution also exhibits a power law expansion at early times, and the energy density of the scalar fields mimics that of the stiff matter.

The extra-intracranial bypass has been used in the treatment of patients with chronic cerebrovascular insufficiency. More recent studies have demonstrated the benefit of this technique to patients with arterial occlusion in PALAVRAS-CHAVEEncéfalo, revascularização cerebral, acidente vascular cerebral, aneurisma dissecante.