具有衰变暗物质的宇宙演化：一种积分方程方法
Cosmological evolution with decaying dark matter: an integral-equation approach
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中文总结 AI 辅助
研究提出CLASSIER-DDM扩展，通过积分方程方法实现衰变暗物质模型。详细描述数值实现，少量迭代可达高精度收敛，运行时间短，无需玻尔兹曼层级和流体近似，确立积分方程方法为模拟非冷遗迹的有效框架。
中文摘要 AI 辅助
我们提出了CLASSIER-DDM，它是玻尔兹曼求解器CLASSIER的扩展，通过积分方程方法实现了衰变暗物质（DDM）模型。该代码处理暗物质粒子到两个任意质量的较轻衰变产物的一般两体衰变，自然涵盖无质量（暗辐射）和有质量（温暗物质）的衰变产物，其微扰通过迭代求解的积分方程来评估。我们详细描述了数值实现，包括背景演化、迭代微扰演化和小尺度解析近似。在相关观测参数空间中，少量迭代就能在物质功率谱和CMB透镜功率谱中实现亚0.1%的收敛。我们发现，对于衰变产物微扰，一百个动量箱足以在高达$k \sim 3\,{\rm Mpc}^{-1}$的今天的物质功率谱中达到$\mathcal{O}(0.1\%)$的精度。该代码每次评估的运行时间为$\mathcal{O}(1\,{\rm min})$，既不需要玻尔兹曼层级也不需要任何流体近似，使得用DDM模型进行参数估计在数值上易于处理。我们还讨论了DDM对宇宙学可观测量的影响，重点是两个有质量衰变产物的情况。这项工作进一步确立了积分方程方法作为宇宙学微扰理论中模拟非冷遗迹的通用且高效框架。
英文摘要
We present CLASSIER-DDM, an extension of the Boltzmann solver CLASSIER that implements the decaying dark matter (DDM) model via its integral-equation approach. The code handles generic two-body decays of a dark matter particle into two lighter decay products with arbitrary masses, naturally encompassing both massless (dark radiation) and massive (warm) decay products, with their perturbations evaluated via integral equations solved iteratively. We describe the numerical implementation in detail, including the background evolution, the iterative perturbation evolution, and a small-scale analytic approximation. A modest number of iterations is sufficient to achieve sub-$0.1\%$ convergence in the matter power spectrum and the CMB lensing power spectrum across the observationally relevant parameter space. We find that a hundred momentum bins for the decay product perturbations are sufficient to achieve $\mathcal{O}(0.1\%)$ accuracy in the matter power spectrum today up to $k \sim 3\,{\rm Mpc}^{-1}$. The code achieves $\mathcal{O}(1\,{\rm min})$ runtimes per evaluation, requiring neither a Boltzmann hierarchy nor any fluid approximation, making parameter estimation with the DDM model numerically tractable. We also discuss the impact of DDM on cosmological observables, focusing on the case of two massive decay products. This work further establishes the integral-equation approach as a versatile and efficient framework for modeling non-cold relics in cosmological perturbation theory.
