Within the framework of canonical type-I seesaw, a feebly interacting massive particle (FIMP) χ is introduced as a dark matter candidate. The leptogenesis mechanism and dark matter relic density share a common origin via decays of Majorana neutrinos N. Provided an additional species φ whose energy density red-shifts as ρ_φ ∝ a ^-(4+n), the Hubble expansion rate is larger than the standard scenario, i.e., the Universe expands faster. The consequences of such a fast expanding Universe (FEU) on leptogenesis as well as FIMP dark matter are investigated in detail. We demonstrate a significant impact on the final baryon asymmetry and dark matter abundance due to the existence of φ for the strong washout scenario. While for the weak washout scenario, the effects of FEU are relatively small. We introduce scale factors F_L and F _χ to describe the corresponding effects of FEU. A semi-analytical approach to derive the efficiency factors η _L and η_χ in FEU is also discussed. The viable parameter space for success thermal leptogenesis and correct FIMP DM relic density is obtained for standard cosmology and FEU. Our results show that it is possible to distinguish different cosmology scenarios for strong washout cases.

在典型 I 型跷跷板的框架内，引入了微弱相互作用的大质量粒子 (FIMP) χ 作为暗物质候选者。轻质发生机制和暗物质遗迹密度通过马约拉纳中微子 N 的衰变具有共同的起源。提供了一个额外的物种 φ，其能量密度红移为 ρ _φ ∝ a ^{-(4+ n )}，哈勃膨胀率大于标准情景，即宇宙膨胀得更快。详细研究了如此快速膨胀的宇宙 (FEU) 对轻质形成以及 FIMP 暗物质的影响。我们证明了对最终重子不对称性和暗物质丰度的显着影响，因为在强冲刷场景中存在 φ。而对于弱冲刷场景，FEU 的影响相对较小。我们引入尺度因子F _L 和F _χ来描述 FEU 的相应影响。_{导出效率因子 η L}和 η _χ的半解析方法 在 FEU 中也进行了讨论。为标准宇宙学和 FEU 获得了成功的热纤体生成和正确的 FIMP DM 遗物密度的可行参数空间。我们的结果表明，有可能区分不同的宇宙学场景以应对强冲刷情况。