Rick's Cosmology Tutorial: Chapter 2B Abstract

The Flatness Problem

The ratio of the universe's average density to the critical density (Omega) has been shown in Chapter 2 to diverge away from its initial value of unity as the universe evolves. In this Chapter it is shown how very rapidly it diverges away from unity. It is shown that in order for Omega to lie in the range 0.1 to 2.0 today, it would have had to equal unity to an accuracy of 15 decimal places at 1 second. In fact, from observational evidence, Omega is believed to be within 1% or so of unity even today. The extreme fine tuning of Omega to be unity at early times is known as the "Flatness Problem". It is shown that an Omega of unity is equivalent to zero net energy, i.e. the gravitational potential energy cancelling with the positive energies. This is perhaps the most stunning realisation about the universe - that it adds up to nothing. The universe is the ultimate free lunch (Guth).

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Tycho's Supernova Remnant (1572). This is a false-colour x-ray image: Red 0.95-1.26 keV, Green 1.63-2.26 keV, Blue 4.1-6.1 keV, J.Warren & J.Hughes (Chandra X-Ray Observatory, NASA)