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An explanation for the observed scale invariants in the universe is presented. Force-free magnetic vortex filaments are proposed to play a crucial role in the formation of superclusters, clusters, galaxies, and stars by initiating gravitational compression. The critical velocities involved in vortex formation are shown to explain the observed constant orbital velocities of clusters, galaxies, and stars. A second scale invariant nr = C where n is particle density and r is average distance between objects, is also noted here and explained by our model. The model predicts a maximum size for magnetic vortices, which is comparable to the dimensions of the observable universe and a density for such vortices which is close to that actually observed, eliminating any theoretical need for missing mass. On this basis, we present an alternative cosmology to that of the "Big Bang," one which provides a much better fit to recent observations of large-scale structure and motion. The model suggests scale invariants between microscopic and cosmological scales, leading to the derivation of a simple analytical expression for the fundamental constants G, mp/me, and e2/hc. We conclude that these expressions indicate the existence of vortex phenomena on the particle level.