The Wave Function Discord

Linde’s proposal of a Euclidean path integral with the “wrong” sign of Euclidean action is often identified with the tunneling proposal for the wave function of the universe. However, the two proposals are in fact quite different. I illustrate the difference and point out that recent criticism by Hawking and Turok does not apply to the tunneling proposal. The debate about the form of the wave function of the universe has recently intensified [1–5]. Its most recent round was initiated by Bousso and Hawking [1] who claimed that the tunneling proposal for the wave function of the universe leads to a catastrophic instability of de Sitter space with respect to pair-production of black holes. This claim was analyzed in Ref. [2] and was shown to be unfounded. Linde [3] has argued that in models of quantum creation of an open universe, the Hartle-Hawking wave function leads to unacceptably low values of the density parameter, and therefore the tunneling proposal should be preferred. In response, Hawking and Turok [4] asserted that with the choice of the tunneling wave function, all perturbations about a homogeneous cosmological background become unstable and therefore this wave function can be meaningfully defined only in homogeneous minisuperspace models. This led them to conclude that the Hartle-Hawking wave function is the only proposal ”with some pretentious to completeness” [5]. While the level of rhetoric is high, I think the progress on this issue may be helped by pointing out that what goes under the name of ”tunneling wave function” are in fact two completely different wave functions. The debate will certainly gain in clarity if this fact is fully recognized. Let me now briefly review the different proposals. The Hartle-Hawking wave function is given by the integral [6]