  Recent arguments show that some curvaton field may generate the cosmological
curvature perturbation. As the curvaton is independent of the inflaton field,
there is a hope that the fine-tunings of inflation models can be cured by the
curvaton scenario. More recently, however, D.H.Lyth discussed that there is a
strong bound for the Hubble parameter during inflation even if one assumes the
curvaton scenario. Although the most serious constraint was evaded, the bound
seems rather crucial for many models of a low inflation scale. In this paper we
try to remove this constraint. We show that the bound is drastically modified
if there were multiple stages of inflation.
