Open universes, eternal inflation, and the anthropic principle (Q1972101)

In modern cosmology, models of open inflation with a variable density parameter \(\Omega\) provide the most natural way to reconcile an open universe with inflation. The use of the anthropic principle is of key importance for the derivation of observational predictions for such models. The author's favorite version of the anthropic principle is called the ``principle of mediocrity''. It extends the Copernican principle which asserts that the position of humans in space is not special, while the principle of mediocrity asserts that the values of the cosmological parameters to be measured are not special either. The paper under review establishes that this principle can be used in a quantitative way to determine the most probable value of \(\Omega\). Applications to more general models of eternal inflation are also discussed.