Cosmological simulations play a crucial role in elucidating the effect of
physical parameters on the statistics of fields and on constraining parameters
given information on density fields. We leverage diffusion generative models to
address two tasks of importance to cosmology -- as an emulator for cold dark
matter density fields conditional on input cosmological parameters $\Omega_m$
and $\sigma_8$, and as a parameter inference model that can return constraints
on the cosmological parameters of an input field. We show that the model is
able to generate fields with power spectra that are consistent with those of
the simulated target distribution, and capture the subtle effect of each
parameter on modulations in the power spectrum. We additionally explore their
utility as parameter inference models and find that we can obtain tight
constraints on cosmological parameters.

以宇宙学为背景，利用扩散生成模型进行冷暗物质密度场的模拟，研究宇宙学参数和功率谱之间的关系以及参数推断的准确性。

宇宙场模拟与扩散模型的参数推断

Cosmological Field Emulation and Parameter Inference with Diffusion  Models

Cold dark matter (CDM) constitutes most of the matter in the Universe. The
interplay between dark and luminous matter in dense cosmic environments like
galaxy clusters is studied theoretically using cosmological simulations.
Observed gravitational lensing is used to test and characterize the properties
of substructures - the small-scale distribution of dark matter - in clusters.
An apt metric, the probability of strong lensing events produced by dark matter
substructure, is devised and computed for 11 galaxy clusters. We report that
observed cluster substructures are more efficient lenses than predicted by CDM
simulations, by more than an order of magnitude. We suggest that hitherto
undiagnosed systematic issues with simulations or incorrect assumptions about
the properties of dark matter could explain our results.

利用宇宙学模拟研究了暗物质和发光物质在星系团等密集宇宙环境中的相互作用。使用观测到的引力透镜现象测试并表征星系团中的小尺度暗物质分布，发现观测到的团簇物质结构比暗物质模拟所预测的更加有效，我们认为这可能是由于模拟存在系统问题或对暗物质属性的错误假设导致的。

在星系团中观测到小尺度引力透镜过多

An excess of small-scale gravitational lenses observed in galaxy  clusters

N-body simulations of Cold Dark Matter (CDM) have shown that, in this
hierarchical structure formation model, dark matter halo properties, such as
the density profile, the phase-space density profile, the distribution of axial
ratio, the distribution of spin parameter, and the distribution of internal
specific angular momentum follow `universal' laws or distributions. Here we
study the properties of the first generation of haloes in a Hot Dark Matter
(HDM) dominated universe, as an example of halo formation through monolithic
collapse. We find all these universalities to be present in this case also.
Halo density profiles are very well fit by the Navarro et al (1997) profile
over two orders of magnitude in mass. The concentration parameter depends on
mass as $c \propto M^{0.2}$,reversing the dependence found in a hierarchical
CDM universe. However, the concentration-formation time relation is similar in
the two cases: earlier forming haloes tend to be more concentrated than their
later forming counterparts. Halo formation histories are also characterized by
two phases in the HDM case: an early phase of rapid accretion followed by
slower growth. Furthermore, there is no significant difference between the HDM
and CDM cases concerning the statistics of other halo properties: the
phase-space density profile; the velocity anisotropy profile; the distribution
of shape parameters; the distribution of spin parameter, and the distribution
of internal specific angular momentum are all similar in the two cases. Only
substructure content differs dramatically. These results indicate that mergers
do not play a pivotal role in establishing the universalities, thus
contradicting models which explain them as consequences of mergers.

通过第一代暗物质（热暗物质）星系的形成，研究了暗物质星系的普遍性与合并事件的关系，结果表明合并事件并不是导致暗物质星系普遍性的关键因素。