Regulating Eternal Inflation II: The Great Divide

TL;DR

This paper refutes a previous conjecture about tunneling discontinuities in eternal inflation, showing instead that potential landscapes split into regions with different stability properties at zero cosmological constant.

Contribution

It demonstrates that tunneling amplitudes are continuous at zero vacuum energy, clarifying the structure of potential landscapes relevant to eternal inflation.

Findings

No discontinuity in tunneling amplitudes at zero cosmological constant

Potential landscapes split into stable and unstable regions at zero vacuum energy

Implications for theories of supersymmetry breaking remain unchanged

Abstract

In a previous paper, two of the authors presented a "regulated" picture of eternal inflation. This picture both suggested and drew support from a conjectured discontinuity in the amplitude for tunneling from positive to negative vacuum energy, as the positive vacuum energy was sent to zero; analytic and numerical arguments supporting this conjecture were given. Here we show that this conjecture is false, but in an interesting way. There are no cases where tunneling amplitudes are discontinuous at vanishing cosmological constant; rather, the space of potentials separates into two regions. In one region decay is strongly suppressed, and the proposed picture of eternal inflation remains viable; sending the (false) vacuum energy to zero in this region results in an absolutely stable asymptotically flat space. In the other region, we argue that the space-time at vanishing cosmological constant is unstable, but not asymptotically Minkowski. The consequences of our results for theories of supersymmetry breaking are unchanged.