What can the observation of nonzero curvature tell us?

Understand

The eternally inflating multiverse provides a consistent framework to understand coincidences and fine-tuning in the universe.

• As such, it provides the possibility of finding another coincidence: if the amount of slow-roll inflation was only slightly more than the anthropic threshold, then spatial curvature might be measurable.
• We study this issue in detail, particularly focusing on the question: "If future observations reveal nonzero curvature, what can we conclude?" We find that whether an observable signal arises or not depends crucially on three issues: the cosmic history just before the observable inflation, the measure adopted to define probabilities, and the nature of the correlation between the tunneling and slow-roll parts of the potential.
• We find that if future measurements find positive curvature at \Omega_k < -10^-4, then the framework of the eternally inflating multiverse is excluded with high significance.