An oscillatory big-bang singularity

The big-bang singularities in the exact cosmological solutions of the Einstein field equations that have been studied up to now are power asymptotes in the sense that all scalar polynomials in the curvature tensor diverge monotonically as a power of clock time along the fundamental world lines, as the singularity is approached. One can thus regard the solutions as being asymptotically self-similar near the singularity. In this paper, we illustrate a more complicated type of singularity by giving an example of an exact cosmological solution in which the big-bang singularity is of an oscillatory nature, so that the solution is not asymptotically self-similar.