arXiv 2202.110772022-02-22astro-ph.CO

宇宙结构形成的动力学场论

Kinetic Field Theory for Cosmic Structure Formation

Sara Konrad, Matthias Bartelmann

备注：: 64 pages, 25 figures, draft prepared for submission to La Rivista del Nuovo Cimento
DOI：: 10.1007/s40766-022-00037-y

摘要：

我们将动力学场论应用于非线性宇宙结构的形成。动力场论将宇宙密度场分解为粒子，并遵循它们在相空间中的轨迹。我们假设初始粒子动量是从高斯随机场中提取的。我们特别强调晚的时间，渐近行为的低阶统计措施的粒子在配置和速度空间中的分布在小的空间尺度上。我们的主要结果是，在沿着Zel'dovich轨迹自由流动的粒子系综中，密度和速度涨落的功率谱随着波数$k$渐近地下降，就像$k\to\infty$的$k^{-3}$一样，与宇宙学模型和假设的暗物质类型无关，其指数仅由空间维度的数量设定。如果在平均场近似下考虑粒子间的相互作用，这个结论对密度涨落功率谱仍然有效。我们还证明了在相同的一般条件下，自由流粒子的双谱像$k^{-11/2}$一样渐近地下降。

英文摘要：

We apply kinetic field theory to non-linear cosmic structure formation. Kinetic field theory decomposes the cosmic density field into particles and follows their trajectories through phase space. We assume that initial particle momenta are drawn from a Gaussian random field. We place particular emphasis on the late-time, asymptotic behaviour on small spatial scales of low-order statistical measures for the distribution of particles in configuration and velocity space. Our main result is that the power spectra for density and velocity fluctuations in ensembles of particles freely streaming along Zel'dovich trajectories asymptotically fall off with wave number $k$ like $k^{-3}$ for $k\to\infty$, irrespective of the cosmological model and the type of dark matter assumed, with the exponent set only by the number of spatial dimensions. This conclusion remains valid for density-fluctuation power spectra if particle interactions are taken into account in a mean-field approximation. We also show that the bispectrum of freely-streaming particles falls off asymptotically like $k^{-11/2}$ under the same general conditions.

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