$V'' < H^{2}$, which leads to generation of density perturbations $O(1)$ on the curvature scale. Therefore if the subsequent stage of the slow-roll inflation is short, we would see enormously large CMB perturbations on the horizon. This would dramatically contradict the results of the cosmological observations, unless the subsequent stage of inflation is very long, which makes the universe flat, $\Omega = 1$.

It is possible to overcome this problem and find single-field models where CDL instantons lead to tunneling and subsequent inflation. Up to now, only one explicit model of this type was proposed [@Linde:1998iw; @Linde:1999wv], but the inflaton potential of this model is quite complicated. The scalar perturbations ignoring the self-gravity of these fluctuations in single-field models has been considered in [@Sasaki:1993ha; @Ratra:1994vw; @Bucher:1994gb; @Sasaki:1994yt; @Lyth:1995cw; @Yamamoto:1995sw; @Bucher:1995ga]. As for the tensor perturbations, the studies in which the perturbation of the scalar field was neglected were done in [@Tanaka:1997kq; @Sasaki:1997ex; @Bucher:1997xs; @Hertog:1999kg]. The general formula for the power spectrum for the single-field open inflation was given in [@Garriga:1998he; @Garriga:1997wz].

It is much simpler to construct models with two fields, where the stage of the slow-roll governed by one of the fields is synchronized by the tunneling of another 