Although natural inflation is a theoretically well-motivated model for cosmic inflation, it is in tension with recent Planck cosmic microwave background anisotropy measurements. We present a way to alleviate this tension by considering a very weak nonminimal coupling of the inflaton field to gravity in both contexts of metric and Palatini formulations of general relativity. We start our discussions with a generic form of the inflaton coupling to the Ricci scalar, then focus on a simple form to do phenomenological study. Our results show that such an extension can bring natural inflation's predictions to a good agreement with the Planck data. Depending on values of the coupling constant ξ and the symmetry breaking scale f, we find that with |ξ|∼ 10^-3 and f≳ 2.0 M_pl predictions of the model stay inside 68% CL allowed region until f increases up to 7.7 M_pl, then only inside 95% CL region after f exceeds the latter value. The predictions from the metric and the Palatini theories are very similar due to the simple form of the coupling function we use and the small magnitude of the coupling ξ. Successful reheating can also be realized in this model.

尽管自然暴胀在理论上是一个很好的宇宙暴胀模型，但它与最近的普朗克宇宙微波背景各向异性测量存在矛盾。我们提出了一种通过在广义相对论的度量和帕拉蒂尼公式的上下文中考虑膨胀场与重力的非常弱的非最小耦合来缓解这种紧张的方法。我们从暴胀子耦合到 Ricci 标量的通用形式开始讨论，然后专注于一个简单的形式来进行现象学研究。我们的结果表明，这样的扩展可以使自然通货膨胀的预测与普朗克数据很好地吻合。根据耦合常数 ξ 和对称破坏尺度 f 的值，我们发现 |ξ|∼ 10 ^-3和 f≳ 2.0 M _pl模型的预测保持在 68% CL 允许区域内，直到 f 增加到 7.7 M _pl，然后只有在 f 超过后一个值之后才在 95% CL 区域内。由于我们使用的耦合函数的简单形式和耦合 ξ 的小幅度，度量和帕拉蒂尼理论的预测非常相似。在此模型中也可以实现成功的再加热。