By writing the running of the scalar spectral index completely in terms of the scalar index ns and the tensor-to-scalar ratio r we are able to impose constraints to models of inflation which are independent of the parameters of the model in question. We write analytical expressions for the running index of Natural Inflation, two models of the type Mutated Hilltop Inflation and the Starobinsky model. The resulting formulae for the running depend exclusively on ns and/or r and will keep tightening the running index further as additional conditions and observations constrain the scalar and the tensor-to-scalar indices.

中文翻译：

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独立于模型参数的运行索引约束

通过完全根据标量指数编写标量谱指数的运行ns和张量标量比r我们能够对与所讨论模型的参数无关的膨胀模型施加约束。我们为自然通货膨胀的运行指数编写了分析表达式，两个模型类型为突变山顶通货膨胀和 Starobinsky 模型。运行的结果公式完全取决于ns和/或r并将继续收紧运行指数，因为附加条件和观察会限制标量和张量到标量指数。