Spinodal effect in the natural inflation model

Recently, Cormier and Holman pointed out that fluctuations of an inflaton field φ are significantly enhanced in the model of spinodal inflation with a potential V(φ) for which the second derivative V⁽²⁾(φ) changes sign. As an application of this model, we investigate particle production in the natural inflation model with a potential V(φ)=m⁴[1 + cos(φ/f)] by making use of the Hartree approximation. For typical mass scales f ∼m_pl∼10¹⁹ GeV and m∼m_GUT∼10¹⁶ GeV, we find that the growth of fluctuations relevantly occurs for the initial value of inflaton φ(0)≲0.1m_pl. Especially for φ(0)≲10^-6m_pl, maximum fluctuations are so large that secondary inflation takes place by produced fluctuations. In this case, the achieved number of e-foldings becomes much larger than in the case where an effect of spinodal instability is neglected.