Abstract
The dynamical evolution of FRW cosmologies, minimally coupled to a finite set of scalar fields with an arbitrary potential, is studied. The general properties of the scale factor and the scalar fields, which are independent of the potential, are determined. It is shown that for k = 0, −1 the evolution of the Hubble function is growing, independently of thepotential, which allows expansive and contractive evolutions of the scale factor. Moreover, if the potential can take negative values, cyclic universes are possible. In the spherical geometry case, k = 1, the existence of expansive, contractive, or cyclic, universes is possible, independently of the condition stated above, namely that the potential would necessarily take negative values. Moreover, the existence of chaotic solutions can be obtained via a fine-tuning.
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