Inflation in a renormalizable cosmological model and the cosmic no-hair conjecture

The possibility of having inflation in a renormalizable cosmological model is investigated. The cosmic no-hair conjecture is proved to hold for all Bianchi types except Bianchi type IX. By the use of a conformal transformation on the metric we show that these models are equivalent to the ones described by the Einstein-Hilbert action for gravity minimally coupled to a set of scalar fields with inflationary potentials. Henceforth, we prove that inflationary solutions behave as attractors in solution space, making it a natural event in the evolution of such models