Spinodal effect in the natural inflation model

Abstract

Recently, Cormier and Holman pointed out that fluctuations of an inflaton field $\varphi$ are significantly enhanced in the model of {\it spinodal inflation} with a potential $V(\varphi )$ for which the second derivative $V^{(2)}(\varphi )$ changes sign. As an application of this model, we investigate particle production in the natural inflation model with a potential $V(\varphi )=m^4[1+\cos (\varphi /f)]$ by making use of the Hartree approximation. For typical mass scales $f\sim m_{\mathrm{pl}}\sim 10^{19}$GeV, and $m\sim m_{\mathrm{GUT}}\sim 10^{16}$GeV, we find that growth of fluctuations relevantly occurs for the initial value of inflaton $\varphi (0)<0.1m_{\mathrm{pl}}$. Especially for $\varphi (0)<10^{-6}{m}_{\mathrm{pl}}$, 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.

16pages, 5figures

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