Primordial Spectrum and Omega_0-Problem in a Power-Law Inflation

The possibility of defining a valid power-law inflationary model of an open universe with a primordial density fluctuation spectrum flatter than a scale-invariant spectrum is examined. The model is developed by relaxing the Big Bang requirements of exponential growth and no divergence from the perturbation specific binding energy. The accelerated expansion of the power-law model satisfies the horizon conditions of a Friedmann universe. An expression is found for relating the observed density parameter (about 10 percent) to the parameter at the moment of the inflationary phase. A natural large-scale cutoff is found to arise for the perturbations during inflation. The analysis supports a model of the universe as dominated by cold dark matter, and identifies problems inherent in a purely baryonic universe and in interpretation of clustering on the basis of analysis of the cosmic microwave background radiation.