Singular instantons and extra dimensions (Q1972094)

Assuming that the universe is homogeneous, isotropic, and \(\Omega\sim 1\), \textit{S. W. Hawking} and \textit{N. Turok} [Phys. Lett. B 425, 25-32 (1998); Phys. Lett. B 432, 271-278 (1998)], have recently suggested that an open universe can be created from nothing using instanton processes without the need of a false vacuum phase. This approach leads to open inflation without the necessity of assuming a special potential. Moreover, since the Hawking-Turok Euclidean action of the instanton is integrable, they were able to use instantons to assign probabilities to different open universes. However, as pointed out by \textit{A. Vilenkin} [Phys. Rev. D 47, 7069-7070 (1998)], and others, the instanton has a singular boundary which would lead to the immediate decay of flat space (as the dimensional reduction of a 5-dimensional non-singular instanton). In the present note, the author presents a lucid discussion of these results and offers several alternate interpretations. It is suggested that the unsuppressed instability of flat space can be traded for metastability with a slow decay rate whenever the size of the extra dimension is large compared with the Planck scale. Contents include: an introduction; decay of flat space; inflation; cosmological perturbations and CMB anisotropies; conclusions; and a 16 item bibliography.