  We study limits of vacuum, isotropic universes in the full, effective,
four-dimensional theory with higher derivatives. We show that all flat vacua as
well as general curved ones are globally attracted by the standard, square root
scaling solution at early times. Open vacua asymptote to horizon-free, Milne
states in both directions while closed universes exhibit more complex
logarithmic singularities, starting from initial data sets of a possibly
smaller dimension. We also discuss the relation of our results to the
asymptotic stability of the passage through the singularity in ekpyrotic and
cyclic cosmologies.
