辐射纪元能否回溯到大爆炸？二次引力中的暗物质产生与遗迹引力子背景
Might the radiation era extend back to the Big Bang? On dark matter production and the relic graviton background in quadratic gravity
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- Higgs Centre for Theoretical Physics（希格斯理论物理中心）
- Perimeter Institute for Theoretical Physics（珀米特理论物理研究所）
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中文总结 AI 辅助
本文在二次引力框架下重新审视辐射纪元回溯至大爆炸的后果，发现暗物质质量与引力子耦合系数的新关系，并提出暗物质引力产生机制，同时指出遗迹引力子背景可约束理论参数。
中文摘要 AI 辅助
基于爱因斯坦引力（拉格朗日量为$\frac{1}{2}M_{pl}^{2}(R-2\Lambda)$）的朴素估计表明，如果辐射纪元回溯到大爆炸（即回溯到经典时空背景仍有意义的极限），这将导致暗物质过度产生以及热引力子的遗迹宇宙背景。本文在二次引力中重新审视这些结论，二次引力是爱因斯坦引力的最小可重整化完备化，其拉格朗日量还包含项$\frac{1}{6}f_0^{-2}R^2-\frac{1}{2}f_{2}^{-2}C^{2}$。假设辐射纪元确实回溯到大爆炸，我们发现系数$f_{2}$与暗物质质量$m_{dm}$之间存在一个新的关系，该关系对于获得正确的暗物质丰度是必需的。这产生了一种新的暗物质引力产生机制（例如，稳定的右手中微子）。此外，遗迹引力子背景的存在与否（可通过其对$N_{\rm eff}$的微小印记被即将进行的CMB实验探测到）将对$f_{0}, f_{2}$施加新的约束。
英文摘要
Naive estimates based on Einstein gravity with Lagrangian $\frac{1}{2}M_{pl}^{2}(R-2Λ)$ suggest that, if the radiation era extended back to the Big Bang (i.e., as far back as the classical spacetime background makes sense), this would result in an over-production of dark matter and a relic cosmic background of thermal gravitons. Here we revisit these conclusions in quadratic gravity, the minimal renormalizable completion of Einstein gravity, whose Lagrangian also includes the terms $\frac{1}{6}f_0^{-2}R^2-\frac{1}{2}f_{2}^{-2}C^{2}$. Assuming the radiation era does extend back to the bang, we find a novel relation between the coefficient $f_{2}$ and the dark matter mass $m_{dm}$, needed to obtain the correct dark matter abundance. This yields a new gravitational production mechanism for dark matter (e.g., stable right-handed neutrinos). Moreover, the presence or absence of the relic graviton background (detectable by forthcoming CMB experiments via its small imprint on $N_{\rm eff}$) will place new constraints on $f_{0}, f_{2}$.
