标题： 一致的$D\to 4$爱因斯坦-高斯-博内引力中慢滚膨胀的功率谱 显示英文标题

标题： Power Spectra of Slow-Roll inflation in the consistent $D\to 4$ Einstein-Gauss-Bonnet gravity

摘要： 人们普遍认为，在极高能量尺度下发生的缓慢滚动物理膨胀对经典广义相对论（GR）的高阶曲率修正非常敏感。本文研究了高阶曲率项——高斯-博内（GB）项对一致的$D \to 4$爱因斯坦高斯-博内（4EGB）引力中的缓慢滚动膨胀原始标量和张量谱的影响。通过在极限$ D\to 4$下重新调整高斯-博内耦合常数$\alpha \to \alpha/(D-4)$，将高斯-博内项引入引力动力学。为了我们的目的，我们利用三阶一致渐近近似方法，明确计算了在缓慢滚动近似下一阶修正准确的原始标量和张量功率谱，以及高斯-博内校正。还计算了标量和张量扰动的谱指数及其指数运行，以及标量与张量谱比值的下一阶缓慢滚动展开结果。这些结果代表了迄今为止文献中获得的最精确的结果。此外，通过研究具有幂律势的模型中，使用普朗克2018限制下的标量谱指数和张量-标量比的理论预测，我们表明二阶校正在未来的测量中非常重要。 显示英文摘要

摘要： The slow-roll inflation which took place at extremely high energy regimes is in general believed to be sensitive to the high-order curvature corrections to the classical general relativity (GR). In this paper, we study the effects of the high-order curvature term, the Gauss-Bonnet (GB) term, on the primordial scalar and tensor spectra of the slow-roll inflation in the consistent $D \to 4$ Einstein Gauss-Bonnet (4EGB) gravity. The GB term is incorporated into gravitational dynamics via the re-scaling of the GB coupling constant $\alpha \to \alpha/(D-4)$ in the limit $ D\to 4$. For our purpose, we calculate explicitly the primordial scalar and tensor power spectra with GB corrections accurate to the next-to-leading order in the slow-roll approximation in the slow-roll inflation by using the third-order uniform asymptotic approximation method. The corresponding spectral indices and their runnings of the spectral indices for both the scalar and tensor perturbations as well as the ratio between the scalar and tensor spectra are also calculated up to the next-to-leading order in the slow-roll expansions. These results represent the most accurate results obtained so far in the literature. In addition, by studying the theoretical predictions of the scalar spectral index and the tensor-to-scalar ratio with Planck 2018 constraint in a model with power-law potential, we show that the second-order corrections are important in future measurements.