[论文解读] Stochastic induced gravitational waves and lowest mass limit of primordial black holes with the effects of reheating

Nilanjandev Bhaumik, Rajeev Kumar Jain|arXiv (Cornell University)|Sep 23, 2020

Cosmology and Gravitation Theories被引用 5

一句话总结

本文研究了在具有偶次多项式势能的单场暴胀模型中，原初黑洞（PBHs）产生的随机引力波（GW）背景，表明由标量曲率扰动产生的次级GW可被未来的空间任务（如LISA和DECIGO）探测到。该研究建立了模型无关的PBH质量下限，并表明非瞬时再加热会使GW谱向更高频移动，甚至已完全蒸发的轻质PBH也能产生可被Advanced LIGO探测到的GW信号。

ABSTRACT

Recently, we have studied the abundance of primordial black holes (PBH) produced in a single field inflationary model with a polynomial potential containing even powers up to the sextic order which allows the existence of an inflection point in the inflaton potential. We found that such a scenario can produce PBHs in a wide range of masses with a nearly monochromatic mass fraction which can account for the total dark matter of the universe in the asteroid mass window. In this paper, we study the stochastic background of gravitational waves (GW) which is inevitably generated in this scenario due to the second order effects caused by large primordial scalar curvature perturbations at the PBHs scales. We find that the resulting secondary background of GWs could be potentially detected by the future space based GWs observatories such as LISA, TAIJI, DECIGO or BBO. Using a model independent approach, we also obtain a lower limit on the PBHs mass by only assuming an instantaneous and a smooth transition from the ultra slow roll to the slow roll phase. Further, we investigate the effects of reheating on the secondary GWs spectrum and find that an epoch of a non-instantaneous reheating can cause a shift in the GWs spectrum to larger frequencies. Interestingly, in this scenario, we also notice that very light PBHs which may completely evaporate by today and would not contribute to the dark matter at all, will still generate a stochastic background of secondary GWs that may be detected by a future design of the ground based Advanced LIGO detector.

研究动机与目标

• 研究具有偶次多项式势能的单场暴胀模型中，原初黑洞（PBHs）产生的随机引力波背景。
• 确定在PBH形成尺度处，由大原初标量曲率扰动产生的次级引力波的可探测性。
• 基于从超慢滚到慢滚暴胀的过渡过程，推导出不依赖模型的PBH质量下限。
• 分析非瞬时再加热对引力波谱的影响，特别是对频率分布的影响。

提出的方法

• 通过引入最高至六次的偶次幂项来建模标量场势能，以产生拐点，从而在宽广的质量范围内实现PBH的形成。
• 计算在PBH形成尺度处，由大原初标量曲率扰动产生的二阶引力波背景。
• 采用不依赖模型的方法，仅基于从超慢滚到慢滚暴胀的过渡动力学，推导出PBH的最小质量下限。
• 将非瞬时再加热效应纳入GW谱中，表明能量密度演化方式的改变导致了频率的移动。
• 将所得的GW功率谱与未来观测台如LISA、TAIJI、DECIGO、BBO以及Advanced LIGO的灵敏度曲线进行比较。
• 评估已完全蒸发至今的PBH所辐射的GW信号在当前或近未来地面探测器灵敏度下的可探测性。

实验结果

研究问题

• RQ1 未来空间观测台如LISA或DECIGO能否探测到原初黑洞产生的次级随机引力波背景？
• RQ2 仅基于从超慢滚到慢滚暴胀的过渡动力学，原初黑洞的最小质量可被多大程度约束？
• RQ3 非瞬时再加热如何影响次级引力波谱的频率分布？
• RQ4 至今已完全蒸发的PBH所辐射的引力波是否仍能被当前或近未来的地面探测器探测到？
• RQ5 在该暴胀情景中，大原初标量曲率扰动在产生随机GW背景中起什么作用？

主要发现

• 由原初黑洞产生的次级随机引力波背景，可能被未来的空间观测台如LISA、TAIJI、DECIGO和BBO探测到。
• 基于从超慢滚到慢滚暴胀的过渡动力学，推导出不依赖模型的原初黑洞质量下限。
• 非瞬时再加热导致引力波谱向更高频发生可测量的移动。
• 即使至今已完全蒸发的原初黑洞，仍能产生可被未来Advanced LIGO探测器设计探测到的随机引力波背景。
• 该情景允许在小行星质量窗口内实现几乎单色的质量分数分布，与总暗物质丰度一致。