Open inflation, the four form and the cosmological constant

Fundamental theories of quantum gravity such as supergravity include a four form field strength which contributes to the cosmological constant. The inclusion of such a field into our theory of open inflation [S.W. Hawking, N. Turok, Phys. Lett. B 425 (1998) 25] allows an anthropic solution to the cosmological constant problem in which cosmological constant gives a small but non-negligible contribution to the density of todayʹs universe. We include a discussion of the role of the singularity in our solution and a reply to Vilenkinʹs recent criticism.