What can the observation of nonzero curvature tell us?
Author(s)Nomura, Yasunori; Guth, Alan
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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 in our past 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 in the eternally inflating spacetime, and the sign and strength of the correlation between the tunneling and slow-roll parts of the potential. We find that if future measurements find positive curvature at the level Ω[subscript k]≲-10[superscript -4], then the framework of the eternally inflating multiverse, as currently understood, is excluded with high significance. If the measurements instead reveal negative curvature at the level Ω[subscript k]≲-10[superscript -4], then we can conclude that (1) diffusive (new or chaotic type) eternal inflation did not occur in our immediate past; (2) our pocket universe was born by a bubble nucleation; (3) the probability measure does not reward volume increase; and (4) the origin of the observed slow-roll inflation is an accidental feature of the potential, presumably selected by anthropic conditions, and not due to a theoretical mechanism ensuring the flatness of the potential. Discovery of Ω[subscript k]≲-10[superscript -4] would also give us nontrivial information about the correlation between the tunneling and slow-roll parts of the potential; for example, a strong correlation favoring large N would be ruled out in certain measures. We also address the question of whether the current constraint on Ωk is consistent with multiverse expectations; we find the answer to be yes, except that current observations, for many choices of measure, rule out the possibility of strong correlations in the potential which favor small values of N. In the course of this work we were led to consider vacuum decay branching ratios, and found that it is more likely than one might guess that the decays are dominated by a single channel. Planned future measurements of spatial curvature provide a valuable opportunity to explore the structure of the multiverse as well as the cosmic history just before the observable inflation.
DepartmentMassachusetts Institute of Technology. Department of Physics; Massachusetts Institute of Technology. Laboratory for Nuclear Science
Physical Review D
American Physical Society
Guth, Alan, and Yasunori Nomura. “What Can the Observation of Nonzero Curvature Tell Us?” Physical Review D 86.2 (2012). © 2012 American Physical Society
Final published version