本文研究具有四次自耦合和中微子指数耦合的 $ν$EDE 模型，考察其能否自然产生约10%的 EDE 能量占比以缓解 $H_0$ 张力，但所测参数均未满足要求。
摘要：
中微子辅助早期暗能量（$ν$EDE）的思想考虑了中微子与用于建模早期暗能量（EDE）的标量场之间的耦合，其提出旨在减少通常 EDE 模型中出现的某些精细调节和巧合问题。为了能够有效缓解 $H_0$ 张力，EDE 对总能量密度的贡献（$f_\ ext{EDE}$）在物质—辐射相等红移附近应约为 10%。对于一个具有 EDE 场四次自耦合以及与中微子指数耦合的模型，我们验证了 $ν$EDE 模型在何种条件下能够满足这些要求。我们发现，在 EDE 场初始被冻结的情形下，其对 $f_\ ext{EDE}$ 的贡献可能显著，但对中微子—EDE 耦合并不敏感，也不能解决 EDE 巧合问题。另一方面，如果 EDE 场在有效势的最小值处已经开始动力学演化，它就会追踪这个随时间变化的最小值；该最小值呈现出一个由中微子从相对论性粒子向非相对论性粒子转变所触发的特征。这一特征在该转变时期附近以自然方式产生 $f_\ ext{EDE}$，而该时期大致与物质—辐射相等红移重合。对于我们所考虑的参数集合，在这一特定 $ν$EDE 模型中，我们没有找到满足背景宇宙学演化要求、从而以自然方式缓解 Hubble 张力的参数值。
英文摘要：
The idea of neutrino-assisted early dark energy ($ν$EDE), where a coupling between neutrinos and the scalar field that models early dark energy (EDE) is considered, was introduced with the aim of reducing some of the fine-tuning and coincidence problems that appear in usual EDE models. In order to be relevant in ameliorating the $H_0$ tension, the contribution of EDE to the total energy density ($f_\text{EDE}$) should be around 10\% near the redshift of matter-radiation equality. We verify under which conditions $ν$EDE models can fulfill these requirements for a model with a quartic self-coupling of the EDE field and an exponential coupling to neutrinos. We find that in the situation where the EDE field is frozen initially, the contribution to $f_\text{EDE}$ can be significant but it is not sensitive to the neutrino-EDE coupling and does not address the EDE coincidence problem. On the other hand, if the EDE field starts already dynamical at the minimum of the effective potential, it tracks this time-dependent minimum that presents a feature triggered by the neutrino transition from relativistic to nonrelativistic particles. This feature generates $f_\text{EDE}$ in a natural way at around this transition epoch, that roughly coincides with the matter-radiation equality redshift. For the set of parameters that we considered we did not find values that satisfy the requirements on the background cosmological evolution to mitigate the Hubble tension in a natural way in this particular $ν$EDE model.
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