论文标题
随机隧道的原始黑洞
Primordial black holes from stochastic tunnelling
论文作者
论文摘要
如果充气量被困在通货膨胀结束前不久的局部最小值，则它通过在称为随机隧道的过程中建立量子波动来逃脱。在这项工作中，我们研究了在这种情况下产生的宇宙学波动，以及它们形成原始黑洞（PBHS）的可能性。这是通过使用随机 - $Δn$形式主义来完成的，这使我们能够重建在false-vacuum状态上花费的$ e $ folds数量的高度非高斯尾巴。我们在分析和数值上探索了两个不同的玩具模型，以确定哪些属性所具有或不取决于false-Vacuum配置文件的细节。我们发现，当潜在的屏障与其宽度相比足够小时，$ΔV/v <δϕ^2/m _ {\ text {pl}}^2 $，可以将潜力近似为平坦的两个局部极端物之间，因此先前获得的结果是在“ $Δv/v/m _ _” $Δv/m _ _ _ {pl pl <v/m _ _ {丰度取决于潜在的障碍的高度，当$ΔV/v> v/m _ {\ text {pl}}^4 $中，超级指数（即作为指数的指数）在后面的情况下允许pbroke flutife toperife files。真空，我们还发现，除非潜力接近线性，否则通常会遇到缓慢的违规行为。
If the inflaton gets trapped in a local minimum of its potential shortly before the end of inflation, it escapes by building up quantum fluctuations in a process known as stochastic tunnelling. In this work we study cosmological fluctuations produced in such a scenario, and how likely they are to form Primordial Black Holes (PBHs). This is done by using the stochastic-$δN$ formalism, which allows us to reconstruct the highly non-Gaussian tails of the distribution function of the number of $e$-folds spent in the false-vacuum state. We explore two different toy models, both analytically and numerically, in order to identify which properties do or do not depend on the details of the false-vacuum profile. We find that when the potential barrier is small enough compared to its width, $ΔV/V < Δϕ^2/M_{\text{Pl}}^2$, the potential can be approximated as being flat between its two local extrema, so results previously obtained in a "flat quantum well'' apply. Otherwise, when $ΔV/V < V/M_{\text{Pl}}^4$, the PBH abundance depends exponentially on the height of the potential barrier, and when $ΔV/V > V/M_{\text{Pl}}^4$ it depends super-exponentially ( i.e. as the exponential of an exponential) on the barrier height. In that later case PBHs are massively produced. This allows us to quantify how much flat inflection points need to be fine-tuned. In a deep false vacuum, we also find that slow-roll violations are typically encountered unless the potential is close to linear. This motivates further investigations to generalise our approach to non-slow-roll setups.
