Spinodal effect in the natural inflation model

Recently, Cormier and Holman pointed out that fluctuations of an inflaton field $\phi$ are significantly enhanced in the model of {\it spinodal inflation} with a potential $V(\phi)$ for which the second derivative $V^{(2)}(\phi)$ changes sign. As an application of this model, we investigate particle production in the natural inflation model with a potential $V(\phi)=m^4 [1+\cos (\phi/f)]$ by making use of the Hartree approximation. For typical mass scales $f \sim m_{\rm pl} \sim 10^{19}$GeV, and $m \sim m_{\rm GUT} \sim 10^{16}$GeV, we find that growth of fluctuations relevantly occurs for the initial value of inflaton $\phi(0)<0.1 m_{\rm pl}$. Especially for $\phi(0)<10^{-6}m_{\rm pl}$, maximum fluctuations are so large that secondary inflation takes place by produced fluctuations. In this case, the achieved number of $e$-folding becomes much larger than in the case where an effect of spinodal instability is neglected. Since low momentum modes are mainly enhanced, this may affect long wave metric perturbations relevant for the structure formation.