On the Properties of the Power-Law Cosmological Solutions in Lovelock Gravity

In this paper we study the properties of Kasner cosmological solutions in Lovelock gravity. Recent progress in the investigation of flat cosmological models in Lovelock gravity unveiled the fact that in quadratic (Gauss–Bonnet) and cubic Lovelock gravities, the higher-order power-law solutions could play the role of both future and past asymptotes, and under some conditions, there could exist a smooth transition between them. So it is natural to question if this feature is unique to Gauss–Bonnet and cubic Lovelock gravities, or if it is a general feature of Lovelock gravity. Our analysis suggests that starting from quartic and in all higher-order Lovelock gravities, the high-order Kasner solution cannot play the role of a past asymptote, not only preventing the abovementioned transition from happening, but also potentially hindering the possibility of reaching viable compactification.