``Old'' locked inflation

In this paper, we revisit the idea of locked inflation, which does not require a potential satisfying the normal slow-roll condition, but suffers from the problems associated with ``saddle inflation''. We propose a scenario based on locked inflation, however, with an alternative evolution mechanism of the ``waterfall field'' . Instead of rolling down along the potential, the field will tunnel to end the inflation stage like in old inflation, by which the saddle inflation could be avoided. Further, we study a cascade of old locked inflation, which can be motivated by the string landscape. Our model is based on the consideration of making locked inflation feasible so as to give a working model without slow roll; It also can be seen as an effort to embed the old inflation in string landscape.