[论文解读] Primordial Black Holes from Supercooled Phase Transitions

Yann Gouttenoire, Tomer Volansky|arXiv (Cornell University)|May 8, 2023

Cosmology and Gravitation Theories被引用 4

一句话总结

本文提出，原初黑洞（PBHs）可在早期宇宙中强超冷化的一级相变期间形成，其中因果区域内的气泡成核延迟导致真空主导持续时间延长，从而产生大的密度对比度。关键结果是当相变持续时间超过哈勃时间的12%（即 β/H ≲ 8）时，PBHs 会大量形成，且其丰度与超冷化持续时间无关，与 de Sitter 无毛猜想一致。

ABSTRACT

Cosmological first-order phase transitions (1stOPTs) are said to be strongly supercooled when the nucleation temperature is much smaller than the critical temperature. These are often encountered in theories that admit a nearly scale-invariant potential, for which the bounce action decreases only logarithmically with temperature. During supercooled 1stOPTs the equation of state of the universe undergoes a rapid and drastic change, transitioning from vacuum-domination to radiation-domination. The statistical variations in bubble nucleation histories imply that distinct causal patches percolate at slightly different times. Patches which percolate the latest undergo the longest vacuum-domination stage and as a consequence develop large over-densities triggering their collapse into primordial black holes (PBHs). We derive an analytical approximation for the probability of a patch to collapse into a PBH as a function of the 1stOPT duration, $β^{-1}$, and deduce the expected PBH abundance. We find that 1stOPTs which take more than $12\%$ of a Hubble time to complete ($β/H \lesssim 8$) produce observable PBHs. Their abundance is independent of the duration of the supercooling phase, in agreement with the de Sitter no hair conjecture.

研究动机与目标

• 研究通过延迟成核在超冷化一级相变（1stOPTs）中形成原初黑洞（PBHs）的机制。
• 量化PBH形成概率作为相变持续时间 β⁻¹ 的函数。
• 确定在宇宙学与天体物理学约束下可观测PBH生成的阈值。
• 推导一个与数值模拟一致的PBH坍缩概率的解析近似公式。

提出的方法

• 将宇宙建模为真空能量（ρ_V）与辐射（ρ_R）的混合，超冷化期间状态方程为 ω = -1。
• 采用单位体积内指数形式的气泡成核速率，Γ_V(t) = Γ₀e^{βt}，其中 β 由成核温度附近的瞬子作用量导出。
• 在指数膨胀下应用因果体积近似，计算晚成核区域的存活概率。
• 利用无先前成核的区域存活概率，推导出坍缩概率 P_coll 作为 β/H_n、δ_c 与哈勃速率的函数。
• 通过数值结果拟合半解析公式 P_coll ≈ exp[−a(β/H_n)^b(1+δ_c)^{cβ/H_n}]，拟合参数为 a≈0.5646，b≈1.266，c≈0.6639。
• 与数值计算结果对比验证，并与基于因果体积和隧穿速率的解析近似进行比较。

Figure 1: The supercooled late-blooming mechanism : a) The nucleation of bubbles through quantum or thermal tunneling is a random process. Within certain causal patches – such as the one delimited with a black dotted circle and labeled “late-bloomer” – bubble nucleation can start later than the back

实验结果

研究问题

• RQ1 在超冷化一级相变期间，具有延迟气泡成核的因果区域坍缩形成原初黑洞的概率是多少？
• RQ2 相变持续时间（β⁻¹）如何影响通过此机制形成的PBH丰度？
• RQ3 PBH丰度在何种阈值下变得可观测？其对超冷化持续时间的依赖关系如何？
• RQ4 坍缩概率如何依赖于密度对比度阈值 δ_c 与相变期间的哈勃速率？
• RQ5 在此PBH形成机制中，de Sitter 无毛猜想在多大程度上成立？

主要发现

• 当相变持续时间超过哈勃时间的12%时，即 β/H ≲ 8，PBHs 会大量形成。
• PBH丰度与超冷化阶段的持续时间无关，与 de Sitter 无毛猜想一致。
• 坍缩概率可用半解析公式 P_coll ≈ exp[−a(β/H_n)^b(1+δ_c)^{cβ/H_n}] 良好近似，拟合参数为 a≈0.5646，b≈1.266，c≈0.6639。
• 数值结果与拟合公式的吻合程度优于基于因果体积与指数速率推导出的解析近似。
• 该机制预测可产生可观测的PBHs，其质量由相变时刻的声学视界决定，受CMB、微引力透镜与引力波约束。
• 该模型可解释具有近似标度不变势的理论中PBH的形成，其中瞬子作用量随温度缓慢减小，从而支持长时间的超冷化阶段。

Figure 2: During a supercooled first-order PT, the universe changes from a vacuum-like equation of state (EoS) with $\omega=-1$ to a radiation EoS with $\omega=1/3$ . Depending on their bubble nucleation history, distinct Hubble patches follow different EoSs. We compare the EoS of the background ( b