Open Inflation With Scalar-tensor Gravity
  The open inflation model recently proposed by Hawking and Turok is investigated in scalar-tensor gravity context. If the dilaton-like field has no potential, the instanton of our model is singular but has a finite action. The Gibbons-Hawking surface term vanishes and hence, can not be used to make $\Omega_0$ nonzero. To obtain a successful open inflation one should introduce other matter fields or a potential for the dilaton-like fields. 
Jae-weon Lee, Seoktae Koh and Chul H. Lee