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arXiv 2308.09286gr-qcastro-ph.CO
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原初黑洞功率谱的 $k^6$ 增长

Power spectrum with $k^6$ growth for primordial black holes

Rongrong Zhai, Hongwei Yu, Puxun Wu

AI总结:

本文研究暴胀中声速与暴胀子滚动速度降低对曲率扰动功率谱的影响,发现声速突变时功率谱仅呈 $k^2$ 增长,而在声速与慢滚参数 $η$ 变化时序的特定条件下,功率谱可达到迄今最陡峭的 $k^6$ 增长,从而在满足宇宙微波背景辐射约束的同时有效产生原初黑洞。

摘要:

暴胀子滚动速度的降低和曲率扰动声速的降低都可以在暴胀期间放大曲率扰动,从而产生可观数量的原初黑洞。在超慢滚暴胀情形中,人们已经发现曲率扰动功率谱具有 $k^4$ 增长。在本文中,我们发现当声速突然降低时,曲率扰动在红外极限下变得依赖于尺度,并且曲率扰动功率谱只具有 $k^2$ 增长。进一步地,通过研究暴胀模型中功率谱的演化——在该模型中曲率扰动的声速和暴胀子的滚动速度同时被降低——我们发现功率谱在大尺度上近似尺度不变,从而满足宇宙微波背景辐射观测的限制,同时可以在小尺度上得到增强,导致原初黑洞的大量形成。在声速与慢滚参数 $η$ 同时改变以及声速的改变先于慢滚参数 $η$ 的改变这两种情形中,在特定条件下功率谱可以具有 $k^6$ 增长,这是迄今所报道的功率谱最陡峭的增长。

英文摘要:

The decrease of both the rolling speed of the inflaton and the sound speed of the curvature perturbations can amplify the curvature perturbations during inflation so as to generate a sizable amount of primordial black holes. In the ultraslow-roll inflation scenario, it has been found that the power spectrum of curvature perturbations has a $k^4$ growth. In this paper, we find that when the speed of sound decreases suddenly, the curvature perturbations becomes scale dependent in the infrared limit and the power spectrum of the curvature perturbation only has a $k^2$ growth. Furthermore, by studying the evolution of the power spectrum in the inflation model, in which both the sound speed of the curvature perturbations and the rolling speed of the inflaton are reduced, we find that the power spectrum is nearly scale invariant at the large scales to satisfy the constraint from the cosmic microwave background radiation observations, and at the same time can be enhanced at the small scales to result in an abundant formation of primordial black holes. In the cases of the simultaneous changes of the sound speed and the slow-roll parameter $η$ and the change of the sound speed preceding that of the slow-roll parameter $η$, the power spectrum can possess a $k^6$ growth under certain conditions, which is the steepest growth of the power spectrum reported so far.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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