AI 中文总结
该研究探究量子引力对贝肯斯坦-霍金熵的对数修正，推导共动曲率扰动演化方程，计算N³LO阶的原初谱，发现修正会改变标量谱倾斜度、张量-标量比及单场一致性关系，为暴胀模型特征研究提供基础。
AI 中文摘要
许多量子引力方法预测贝肯斯坦-霍金熵存在对数修正。在引力的时空热力学描述框架内，此类修正会导出修正后的引力场方程。我们研究这些修正对标准单场慢滚暴胀期间原初扰动的影响，推导共动曲率扰动的演化方程，表明其仍保持标准的Mukhanov–Sasaki形式，量子引力修正通过随时间变化的有效频率引入。我们在哈勃流参数的 next-to-next-to-next-to-leading order（N³LO）阶计算标量和张量原初谱，保留对数修正的主导贡献。标量谱仍近似标度不变，但量子引力修正会改变其倾斜度与跑动；自由张量模式仍如广义相对论中那般传播，不过是在经量子引力修正的背景下。两个 sector 的这种不同响应会改变张量-标量比以及单场一致性关系，这为通过暴胀后演化追踪模型特征并进入宇宙微波背景（CMB）提供了起点。
英文摘要
Many approaches to quantum gravity predict logarithmic corrections to the Bekenstein-Hawking entropy. Within the spacetime-thermodynamic description of gravity, such corrections lead to modified gravitational field equations. We study their effect on primordial perturbations during standard single-field slow-roll inflation. We derive the evolution equation for the comoving curvature perturbation and show that it retains the standard Mukhanov--Sasaki form, with the quantum-gravity correction entering through the time-dependent effective frequency. We compute the scalar and tensor primordial spectra at next-to-next-to-next-to-leading order ($\mathrm{N}^3\mathrm{LO}$) in the Hubble-flow parameters, keeping the leading contribution from the logarithmic correction. The scalar spectrum remains nearly scale invariant, but the quantum-gravity correction shifts its tilt and runnings. Free tensor modes still propagate as in general relativity, although on the quantum-gravity-corrected background. This different response of the two sectors shifts both the tensor-to-scalar ratio and the single-field consistency relation, which provide the starting point for tracing the model's signatures through the post-inflationary evolution and into the CMB.
Comments17 pages + Appendix
