论文标题
关于冷暗物质的宇宙密度 - 透明功率光谱的渐近行为
On the asymptotic behaviour of cosmic density-fluctuation power spectra of cold dark matter
论文作者
论文摘要
我们研究了Zel'Dovich近似中冷暗物质密度波动谱的小规模渐近行为，而无需引入紫外线截止。假设最初相关的高斯随机场和光谱指数$ 0 <n_s <1 $，我们得出了初始动量摩托明相关性的小规模渐近行为。然后使用该结果来得出Zel'Dovich近似中功率谱的渐近学。我们的主要结果是一个渐近系列，以大波浪数在$ k^{ - 3} $尾部主导，其中包含$ k^{n_s-1} $的整数幂和$ k $的对数的高阶术语。此外，我们表明具有紫外线截止的暗物质功率光谱会形成中间范围的尺度范围，在该尺度上，暗物质的渐近学无需截止。这些结果揭示了有关动态场理论中扰动项的基础数学结构的信息，从而揭示了非线性功率谱。我们还讨论了小规模渐近学对频谱索引$ n_s $的敏感性。
We study the small-scale asymptotic behaviour of the cold dark matter density fluctuation power spectrum in the Zel'dovich approximation, without introducing an ultraviolet cut-off. Assuming an initially correlated Gaussian random field and spectral index $0 < n_s < 1$, we derive the small-scale asymptotic behaviour of the initial momentum-momentum correlations. This result is then used to derive the asymptotics of the power spectrum in the Zel'dovich approximation. Our main result is an asymptotic series, dominated by a $k^{-3}$ tail at large wave-numbers, containing higher-order terms that differ by integer powers of $k^{n_s-1}$ and logarithms of $k$. Furthermore, we show that dark matter power spectra with an ultraviolet cut-off develop an intermediate range of scales where the power spectrum is accurately described by the asymptotics of dark matter without a cut-off. These results reveal information about the mathematical structure that underlies the perturbative terms in kinetic field theory and thus the non-linear power spectrum. We also discuss the sensitivity of the small-scale asymptotics to the spectral index $n_s$.
