AI 中文总结
研究用CMB数据测试暴胀情景时超出慢滚区域的预测问题，核心方法是在EGB引力下引入相θ参数化，主要贡献是给出封闭解析映射，证明斯塔罗宾斯基模型预测与最新约束一致并计算遗迹引力波背景及可探测性。
AI 中文摘要
用宇宙微波背景（CMB）数据测试暴胀情景的核心挑战是推导超出慢滚区域仍准确的宇宙学可观测量预测，标准一致性关系在此不再适用。我们在爱因斯坦 - 高斯 - 博内特（EGB）引力背景下，通过引入暴胀动力学的相θ参数化来解决此问题。在此框架内，背景演化以及标量和张量微扰的系数完全用单个单调相变量和哈勃参数表示。这一构建在给定模型的背景参数与相关暴胀可观测量之间提供了封闭的解析映射。该参数化的显著优势是在整个暴胀时期包括暴胀末期都保持正则，传统慢滚一致性关系在此不成立。作为示例应用，我们考虑一个由暴胀子与高斯 - 博内特不变量之间的线性耦合补充的斯塔罗宾斯基型势。使用所提出的形式主义，我们证明斯塔罗宾斯基模型的结果预测与ACT DR6和BICEP/Keck的最新约束一致，明确纳入了非最小高斯 - 博内特耦合对宇宙学微扰参数期望值的影响。最后，我们计算了相应的遗迹随机引力波背景，并评估了其在当前和未来引力波天文台的可探测性。
英文摘要
A central challenge in testing inflationary scenarios with cosmic microwave background (CMB) data is to derive predictions for cosmological observables that remain accurate beyond the slow-roll regime, where the standard consistency relations are no longer applicable. We address this issue in the context of Einstein--Gauss--Bonnet (EGB) gravity by introducing a phase-$θ$ parametrization of the inflationary dynamics. Within this framework, the background evolution and the coefficients governing scalar and tensor perturbations are expressed entirely in terms of a single monotonic phase variable and the Hubble parameter. This construction provides a closed, analytical mapping between the background parameters of a given model and the associated inflationary observables. A notable advantage of the proposed parametrization is that it remains regular throughout the inflationary epoch, including the end-of-inflation regime, in which the conventional slow-roll consistency relations no longer hold. As an illustrative application, we consider a Starobinsky-type potential supplemented by a linear coupling between the inflaton and the Gauss--Bonnet invariant. Using the proposed formalism, we demonstrate that the resulting predictions of the Starobinsky model are consistent with the most recent constraints from ACT DR6 and BICEP/Keck, explicitly incorporating the impact of the non-minimal Gauss--Bonnet coupling on the expected values of the cosmological perturbation parameters. Finally, we compute the corresponding relic stochastic gravitational-wave background and evaluate its detectability with current and forthcoming gravitational-wave observatories.
Comments37 Pages, 10 figures
