发表机构
Baylor University（贝勒大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究在mLQC-I混合方法中构造高精度半解析模式函数，证实有限模式粒子产生与紫外正则性共存，为原初功率谱计算提供基础，相关紫外结论可推广至dressed-metric方法。
AI 中文摘要
我们在mLQC-I的混合方法框架下，为标量宇宙学微扰构造高精度半解析模式函数，以研究紫外正则性与引力粒子产生。演化过程包含渐近的前德西特分支、含量子反弹的前暴胀区域以及暴胀阶段。在中间区域，我们构造了完整的三阶均匀渐近解并引入自适应缺陷校正。三阶近似对代表性高波数模式实现了亚百分之一的复模式精度；缺陷校正后的解在测试的低波数范围内与数值演化的吻合度达到0.00001%的水平。保留振幅与相位为未来原初功率谱及非高斯关联的精密计算提供了可控基础。我们对比了在遥远收缩分支中选取的德西特真空与在反弹处施加的四阶绝热态。有限波数匹配与严格紫外极限需要不同的渐近处理：将主导连接外推至无穷大波数会产生虚假的负频率常数系数与表观紫外发散。相反，大波数德西特模式与四阶绝热展开在能量-动量张量重正化所需的阶数上一致，且光滑的精确演化保留了该紫外结构。有限和中间模式仍可经历非绝热的Bogoliubov混合与粒子产生，因此有限模式的粒子产生与紫外正则性共存。该紫外论证也可推广至 dressed-metric 方法的对应大波数区域，不过定量模式函数需使用其有效质量重新计算。
英文摘要
We construct high-accuracy semi-analytic mode functions for scalar cosmological perturbations in mLQC-I within the hybrid approach to study ultraviolet regularity and gravitational particle creation. The evolution comprises an asymptotic pre-de Sitter branch, a pre-inflationary region containing the quantum bounce, and inflation. In the intermediate region, we construct the complete third-order uniform asymptotic solution and introduce adaptive defect correction. The third-order approximation achieves sub-percent complex-mode accuracy for representative higher-wavenumber modes; defect-corrected solutions agree with numerical evolution at the 0.00001% level over the tested low-wavenumber range. Retaining amplitudes and phases provides a controlled basis for future precision calculations of primordial power spectra and non-Gaussian correlations. We compare the de Sitter vacuum selected in the remote contracting branch with a fourth-order adiabatic state imposed at the bounce. Finite-wavenumber matching and the strict ultraviolet limit require different asymptotic treatments: extrapolating the leading connection to infinite wavenumber yields a spurious constant negative-frequency coefficient and an apparent ultraviolet divergence. Instead, the large-wavenumber de Sitter mode agrees with the fourth-order adiabatic expansion through the order required for energy-momentum tensor renormalization, and smooth exact evolution preserves this ultraviolet structure. Finite and intermediate modes can nevertheless undergo nonadiabatic Bogoliubov mixing and particle creation. Finite-mode particle production thus coexists with ultraviolet regularity. The ultraviolet argument also extends to the dressed-metric approach in its corresponding large-wavenumber regime, while quantitative mode functions must be recalculated using its effective mass.
