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Despite its great popularity, the Big Bang framework for cosmology faces growing contradictions with observation. The Big Bang theory requires three hypothetical entities-the inflation field, nonbaryonic (dark) matter, and the dark energy field-to overcome gross contradictions of theory and observation. Yet, no evidence has ever confirmed the existence of any of these three hypothetical entities. The predictions of the theory for the abundance of 4He, 7Li, and D are more than 7σ from the data for any assumed density of baryons and the probability of the theory fitting the data is less than 10-14. Observations of voids in the distribution of galaxies that are in excess of 100 Mpc in diameter, combined with observed low streaming velocities of galaxies, imply an age for these structure that is at least triple and more likely six times the hypothesized time since the Big Bang. Big Bang predictions for the anisotropy of the microwave background, which now involve seven or more free parameters, still are excluded by the data at the 2σ level. The observed preferred direction in the background anisotropy completely contradicts Big Bang assumptions. In contrast, the predictions of plasma cosmology have been strengthened by new observations, including evidence for the stellar origin of the light elements, the plasma origin of large-scale structures, and the origin of the cosmic microwave background in a "radio fog" of dense plasma filaments. This review of the evidence shows that the time has come, and indeed has long since come, to abandon the Big Bang as the primary model of cosmology.