Within the framework of homogeneous models of the Universe, inflation provides the simplest explanation for the present cosmic isotropy, and a Bianchi type-IX (mixmaster) model is the least prejudiced guess we can make about the state of the Universe before the inflationary phase. However, a mixmaster model would not inflate unless either shear or the radiation energy density are large enough. Particle creation enhances the radiation energy density and therefore enlarges the set of inflating initial conditions for the Universe.