标题： 空间曲率在原初引力波功率谱中的作用 显示英文标题

标题： Role of spatial curvature in the primordial gravitational wave power spectrum

摘要： 本文研究了非零空间曲率对暴胀期间产生的原初引力波传播的影响。 特别是，我们考虑了在均匀且各向同性的背景上的张量扰动，并描述了引力波在具有空间弯曲几何的de Sitter相中的传播。 因此，在开放和封闭宇宙的情况下，我们推导出了视界跨越时的原初功率谱表达式。 然后，我们分析了张量模在暴胀后时代的传播方式，展示了辐射和物质时代转移函数的演化，以及中间阶段的匹配条件。 为了说明不同相对论物种的本质特性，我们还探讨了辐射能量密度标准行为的修正。 为此，我们引入了参与原初能量和熵密度贡献的相对论粒子的有效自由度数。 在次视界近似下，我们以曲率密度参数的形式得到了遗迹引力波的能谱能量密度。 最后，我们讨论了当前和未来实验探测不同频率范围内的原初引力波信号的能力。 显示英文摘要

摘要： This paper investigates the effects of nonvanishing spatial curvature on the propagation of primordial gravitational waves produced during inflation. In particular, we consider tensor perturbations over a homogeneous and isotropic background, and describe the propagation of gravitational waves in the de Sitter phase with spatially curved geometries. We thus derive the expression of the primordial power spectrum at the horizon crossing, in the case of open and closed universes. Then, we analyze how tensor modes propagate in the post-inflationary era, showing the evolution of transfer functions in the radiation and matter epochs, as well as the matching conditions in the intermediate regime. To account for the intrinsic nature of different relativistic species, we also explore the corrections to the standard behavior of the radiation energy density. For this purpose, we introduce the effective number of degrees of freedom of relativistic particles contributing to the primordial energy and entropy densities. Under the subhorizon approximation, we obtain the spectral energy density of relic gravitational waves in terms of the curvature density parameter. Finally, we discuss the capability of present and future experiments to detect the primordial gravitational wave signal at different frequency regimes.