Power law singularities in orthogonal spatially homogeneous cosmologies

We investigate the structure of the so-called power asymptote singularities in orthogonal spatially homogeneous solutions of the Einstein field equations with perfect fluid source. We first give a systematic survey of the different possible power asymptotes, some of which are well known, and some new, and characterize them in a coordinate-independent manner. The known orthogonal spatially homogeneous exact solutions with perfect fluid source are then classified on the basis of which power asymptote they admit. In many cases this leads to simpler forms of the known solutions, and suggests methods for deriving new solutions.