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.