de Sitter nonlinear sigma model and accelerating universe

Abstract

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 Lambda 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 Lambda = 0 as a special case and it discriminate from the standard Lambda-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 omega = -1 both from above and below, but the crossing does not occur. It predicts present value of omega similar to -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.