Anthropic reasons for nonzero flatness and $\Lambda$

In some cosmological theories with varying constants there are anthropic reasons why the expansion of the universe must not be too close to flatness or the cosmological constant too close to zero. Using exact theories which incorporate time variations in $\alpha$ and in G we show how the presence of negative spatial curvature and a positive cosmological constant play an essential role in bringing to an end variations in the scalar fields that drive time changes in these “constants” during any dust-dominated era of a universe’s expansion. In spatially flat universes with $\Lambda =0\mathrm{}$ the fine structure constant grows to a value which makes the existence of atoms impossible.