Spinodal effect in the natural inflation model

TL;DR

This paper explores how spinodal instabilities can significantly enhance fluctuations in natural inflation models, leading to secondary inflation and increased e-foldings, especially for certain initial conditions.

Contribution

It applies the Hartree approximation to analyze particle production in natural inflation with spinodal effects, revealing conditions for secondary inflation.

Findings

Fluctuations grow significantly for initial inflaton values less than 0.1 times the Planck mass.

For very small initial values, fluctuations induce secondary inflation.

Spinodal effects can greatly increase the total number of e-foldings during inflation.

Abstract

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.