Alternative Big Bang models are concerned with the curvature of space. Over the past 20 years there have been three competing models arguing that space may be flat, positively curved, like a ball or negatively curved, like a saddle. The details of these competing hypotheses are explained in the book by Silk, J. (1989) The Big Bang, Freeman, p.90-93.
Increasingly, our understanding of the inflation of the Universe suggests that any initial curvature in the Early Universe would be stretched to absolute flatness during the initial massive expansion of the Universe. Before the idea of inflation came along, cosmologists had the problem that if space is slightly curved at the start, it will become massively curved during expansion. Inflation, however, stretches out any wrinkles, just as blowing up a balloon flattens its surface.
Now, new data from the study of the Cosmic Microwave Background support this view. The results from the balloon-borne microwave telescope experiments Maxima and Boomerang, launched in 1998, provide new observational evidence of variations on the Cosmic Microwave Background.
The crucial cosmological parameter that determines the large-scale curvature of the Universe is the density of the Universe — technically measured as Ω (omega), the total energy density of the Universe, normalised to the critical 'closure' value. Different values of Ω separates the positive curvature of an over-dense Universe from the negative curvature of an under-dense one. In a flat universe the parameter Ω = 1.0. New measurements from the Boomerang experiment reported in April 2000 showed that the value of Ω = 1.06 +/- 0.06 and two weeks later the Maxima results showed that Ω = 0.90 +/- 0.07. These results strongly support a flat Universe and support the inflationary scenario for the very early evolution of the Universe.
Details of the Maxima and Boomerang experiments are given in Peterson, J. (2000) Universe in the balance, New Scientist Magazine, vol 168 issue 2269, (16 Dec) page 26.