AI 中文总结
本文研究慢滚暴胀中均匀密度超曲面上的二次阶有效能量-动量张量，分析其在不同波长区域的规范依赖，发现不同规范在红外、紫外区域的行为差异及结构特征。
AI 中文摘要
我们研究慢滚暴胀期间均匀密度超曲面上标量宇宙学扰动的二次阶有效能量-动量张量（2EMT）。该2EMT由线性度规和暴胀子扰动的二次项构成，因此是一个经规范固定的有效源，而非规范不变可观测量。我们施加完整的标量规范条件δρ=0和E=0，将所有扰动用Bardeen势Ψ表示，并在长波和短波区域计算傅里叶空间中的2EMT。我们区分“严格”红外与紫外极限和“中间”区域。在严格红外极限下，均匀密度结果与共动结果一致；在中间红外区域，主导阶保持不变，而显式有限梯度修正区分两种规范。在紫外区域，由于缓变物质时钟ρ₀'∝ε，2EMT被1/ε增强，且均匀密度2EMT的主导项因拉普拉斯项额外被1/σ₂²（σ₂≡ℋ/k）增强；中间紫外展开使次主导梯度层级明确，且不改变主导项。我们将这些结果与重新计算的纵向、空间平坦及共动表达式对比，这些表达式比早期分析更明确。对比显示规范依赖具有结构：均匀密度和共动切片对绝热超哈勃模式一致，而纵向和空间平坦规范在严格红外被慢滚压制，在中间红外变为梯度主导。
英文摘要
We investigate the quadratic-order effective energy--momentum tensor (2EMT) of scalar cosmological perturbations on uniform-density hypersurfaces during slow-roll inflation. The 2EMT is constructed from terms quadratic in the linear metric and inflaton perturbations, and is therefore a gauge-fixed effective source rather than a gauge-invariant observable. We impose the complete scalar gauge conditions $δρ=0$ and $E=0$, express all perturbations in terms of the Bardeen potential $Ψ$, and evaluate the Fourier-space 2EMT in the long- and short-wavelength domains. We distinguish the ``strict'' infrared and ultraviolet limits from the ``intermediate'' regimes. The uniform-density and comoving results agree in the strict infrared limit. In the intermediate infrared regime, the dominant leading order remains the same, while explicit finite-gradient corrections distinguish the two gauges. In the ultraviolet, the 2EMT is enhanced by $1/ε$ due to the slowly varying matter clock, $ρ_0'\proptoε$, and the leading uniform-density 2EMT terms exhibit an additional enhancement by $1/σ_2^2$ $(σ_2\equiv \cal{H}/k)$ from the Laplacian term. The intermediate ultraviolet expansion makes the subleading gradient hierarchy explicit without changing the leading terms. We compare these results with newly recalculated longitudinal, spatially-flat, and comoving expressions, displayed in a more explicit form than in the earlier analysis. The comparison shows that the gauge dependence is structured: uniform-density and comoving slicings coincide for adiabatic super-Hubble modes, whereas the longitudinal and spatially-flat gauges are {\it slow-roll} suppressed in the strict infrared and become {\it gradient} dominated in the intermediate infrared.
Comments18 pages
