Title: Cosmic Degeneracies II: Structure formation in joint simulations of Warm Dark Matter and $f(R)$ gravity Show Chinese title

Title: 宇宙退化II：温暗物质和$f(R)$引力的联合模拟中的结构形成

Abstract: We present for the first time the outcomes of a cosmological N-body simulation that simultaneously implements a Warm Dark Matter (WDM) particle candidate and a modified gravitational interaction in the form of $f(R)$ gravity, and compare its results with the individual effects of these two independent extensions of the standard $\Lambda $CDM scenario, and with the reference cosmology itself. We consider a rather extreme value of the WDM particle mass ($m_{\rm WDM}=0.4$ keV) and a single realisation of $f(R)$ gravity with $|\bar{f}_{R0}|=10^{-5}$, and we investigate the impact of these models and of their combination on a wide range of cosmological observables with the aim to identify possible observational degeneracies. In particular, we focus on the large-scale matter distribution, as well as on the statistical and structural properties of collapsed halos and cosmic voids. Differently from the case of combining $f(R)$ gravity with massive neutrinos -- previously investigated in Baldi et al. (2014) -- we find that most of the considered observables do not show any significant degeneracy due to the fact that WDM and $f(R)$ gravity are characterised by individual observational footprints with a very different functional dependence on cosmic scales and halo masses. In particular, this is the case for the nonlinear matter power spectrum in real space, for the halo and sub-halo mass functions, for the halo density profiles and for the concentration-mass relation. However, other observables -- like e.g. the halo bias -- do show some level of degeneracy between the two models, while a very strong degeneracy is observed for the nonlinear matter power spectrum in redshift space, for the density profiles of small cosmic voids -- with radius below $\approx 5$ Mpc$/h$ -- and for the voids abundance as a function of the void core density. Show Chinese abstract

Abstract: 我们首次展示了宇宙学N体模拟的结果，该模拟同时实现了温暗物质（WDM）粒子候选者和一种形式为$f(R)$引力的修改引力相互作用，并将其结果与这两个独立于标准$\Lambda $冷暗物质（CDM）情景的扩展单独效果以及参考宇宙学本身进行比较。 我们考虑了一个相当极端的WDM粒子质量值（$m_{\rm WDM}=0.4$keV）以及一个$f(R)$引力的单一实现，其中$|\bar{f}_{R0}|=10^{-5}$，并研究这些模型及其组合对广泛范围的宇宙学可观测量的影响，目的是识别可能的观测退化。 特别是，我们关注大尺度物质分布，以及坍缩晕和宇宙空洞的统计和结构特性。 与结合$f(R)$引力与重中微子的情况不同——此前在Baldi等人（2014）的研究中已经调查过——我们发现，由于WDM和$f(R)$引力具有不同的观测足迹，它们在宇宙尺度和晕质量上的功能依赖性非常不同，因此大多数考虑的可观测量没有显示出显著的退化。 特别是，这适用于实空间中的非线性物质功率谱、晕和子晕质量函数、晕密度剖面以及浓度-质量关系。 然而，其他可观测量——例如，比如 晕bias——在两个模型之间显示出一定程度的退化，而在红移空间中非线性物质功率谱则表现出非常强的退化，对于半径低于$\approx 5$ Mpc$/h$的小宇宙空洞的密度剖面，以及作为空洞核心密度函数的空洞丰度。