论文标题
玻尔兹曼方程的渐近分析暗物质遗物丰度
Asymptotic analysis of the Boltzmann equation for dark matter relic abundance
论文作者
论文摘要
通过匹配的渐近近似构建了控制冷遗物丰度的玻尔兹曼方程的解决方案。当丰度远离其平衡值直到较小的温度时，遗物密度的近似是有效的渐近序列。共鸣和阈值效应在领先顺序中考虑到，除非歼灭横截面在阈值时可以忽略不计，否则被认为可以忽略不计。对先前尝试的结构进行了比较，并冻结了文献中常用的近似值。概述了对高阶匹配的扩展，并讨论了解决相关系统的影响。我们将结果与使用基准模型对遗物丰度的数值确定，并找到一个奇妙的协议。开发的方法还可以作为解决包含无限顺序转折点的广泛问题的解决方案。
A solution to the Boltzmann equation governing the thermal relic abundance of cold dark matter is constructed by matched asymptotic approximations. The approximation of the relic density is an asymptotic series valid when the abundance does not deviate significantly from its equilibrium value until small temperatures. Resonance and threshold effects are taken into account at leading order and found to be negligible unless the annihilation cross section is negligible at threshold. Comparisons are made to previously attempted constructions and to the freeze out approximation commonly employed in the literature. Extensions to higher order matching is outlined, and implications for solving related systems are discussed. We compare our results to a numerical determination of the relic abundance using a benchmark model and find a fantastic agreement. The method developed also serves as a solution to a wide class of problems containing an infinite order turning point.
