Invariant Lyapunov exponents and chaos in cosmology

The precise dynamical nature of the Bianchi type-IX cosmological model has been a subject of debate for a number of years. The lack of congruence between various results, which mainly employ numerical calculations of the spectrum of Lyapunov exponents, has motivated a number of attempts at a gauge-invariant characterization of chaos. Here we critically examine one of these attempts and argue that none of the attempted characterizations so far put forward are completely satisfactory. We also briefly discuss natural gauges in cosmology and distinguish between qualitative and quantitative measures of chaos.