  In this paper, we investigate the no-boundary wave function and the
complex-valued instantons for two-field inflation models that have different
masses. If there is a relatively massive direction, to classicalize the massive
field, the solution should start from the slow direction with relatively larger
vacuum energy. Therefore, the existence of the massive direction implies the
increase of expected $e$-foldings. The most probable $e$-foldings are
approximately $\mathcal{N} \simeq (m_{2}/m_{1})^{2} \times \mathcal{O}(1)$ in
the $m_{1} \ll m_{2}$ limit. Therefore, as long as there is a sufficient mass
hierarchy, the no-boundary wave function can reasonably explain large
$e$-foldings, so to speak more than 50 $e$-foldings.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory