Steepest growth of the power spectrum and primordial black holes
Steepest growth of the power spectrum and primordial black holes
复制标题
DOI：
10.1088/1475-7516/2019/06/028
复制
发表时间：
2018-11
影响因子：
6.4
通讯作者：
C. Byrnes;P. S. Cole;S. Patil
中科院分区：
文献类型：
--
作者：
C. Byrnes;P. S. Cole;S. Patil
我们推导出解析界的形状的原始功率谱的背景下，单场的通货膨胀。特别是，一旦瞬变消失，最陡的可能增长具有ns − 1 = 4的谱指数。它的主要含义是，在一个特定的尺度上的功率谱上的任何约束可以外推到一个扩展的尺度范围内的上限。这对于那些由于原始标量扰动的振幅增强而产生遗迹的模型（如原始黑洞）来说很重要。为了生成它们，功率谱需要比CMB尺度上的观测值大许多数量级-通常通过超慢卷膨胀阶段实现-因此在小尺度上受到额外的约束。我们绘制了所有相关的约束，包括CMB光谱失真和引力波的标量扰动源在二阶。我们展示了这是如何限制PBH的允许质量的，特别是对于LIGO最近探测到的感兴趣的大质量，以及未来观测进一步限制它们的前景。我们表明，任何从近似恒定的慢卷膨胀到功率谱迅速上升的阶段的过渡必然意味着功率的干预下降。我们还展示了如何重建一个潜在的，可以重现一个任意的随时间变化的时间，提供了一个互补的角度来看，如何超慢卷可以实现。
We derive analytic bounds on the shape of the primordial power spectrum in the context of single-field inflation. In particular, the steepest possible growth has a spectral index of ns − 1 = 4 once transients have died down. Its primary implication is that any constraint on the power spectrum at a particular scale can be extrapolated to an upper bound over an extended range of scales. This is important for models which generate relics due to an enhanced amplitude of the primordial scalar perturbations, such as primordial black holes. In order to generate them, the power spectrum needs to grow many orders of magnitude larger than its observed value on CMB scales—typically achieved through a phase of ultra slow-roll inflation—and is thus subject to additional constraints at small scales. We plot all relevant constraints including CMB spectral distortions and gravitational waves sourced by scalar perturbations at second order. We show how this limits the allowed mass of PBHs, especially for the large masses of interest following recent detections by LIGO and prospects for constraining them further with future observations. We show that any transition from approximately constant ϵ slow-roll inflation to a phase where the power spectrum rapidly rises necessarily implies an intervening dip in power. We also show how to reconstruct a potential that can reproduce an arbitrary time-varying ϵ, offering a complementary perspective on how ultra slow-roll can be achieved.