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arXiv · 2404.18548

On the duality in constant-roll inflation

Yue Wang·Qing Gao·Shengqing Gao·Yungui Gong
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Abstract

There is a duality in the observables $n_s$, $r$ and the inflaton potential between large and small $\eta_H$ for the constant-roll inflation if the slow-roll parameter $\epsilon_H$ is negligible. In general, the duality between $\eta_H$ and $\bar{\eta}_H$ does not hold for the background evolution of the inflation. For some particular solutions for the constant-roll inflation with $\eta_H$ being a constant, we find that in the small field approximation, the potential takes the quadratic form and it remains the same when the parameter $\eta_H$ changes to $\bar{\eta}_H=3-\eta_H$. If the scalar field is small and the contribution of $\epsilon_H$ is negligible, we find that there exists the logarithmic duality and the duality between large and small $\eta_H$ for the primordial curvature perturbation in inflationary models with the quadratic potential.

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Yue Wang, Qing Gao, Shengqing Gao, Yungui Gong. 2024-04-29. On the duality in constant-roll inflation. https://arxiv.org/abs/2404.18548

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