标题： 黑洞遗迹与膨胀：蓝扰动谱的限制 显示英文标题

标题： Black Hole Relics and Inflation: Limits on Blue Perturbation Spectra

摘要： 蓝原始功率谱具有谱指数$n>1$，并且在最近提出的混合暴胀场景中自然产生。通过在四极子尺度上规范光谱并考虑原始黑洞蒸发最终阶段形成的普朗克质量遗迹的可能过量生产，得出了对{\em n}的观测上限。在与观测到的四极子各向异性相容的最大再加热温度的膨胀宇宙中，上限是$n=1.4$，但对于较低的再加热温度则稍微弱一些。这个限制适用于57个十年的质量范围，因此对宇宙变化和四极子各向异性的任何引力波贡献都不敏感。它也独立于宇宙的暗物质含量，因此也独立于偏置参数。在某些情况下，在暴胀结束和再加热之间可能存在一个延长的类似尘埃的阶段。在这种情况下，原始黑洞形成得更加丰富，上限是$n=1.3$。 显示英文摘要

摘要： Blue primordial power spectra have spectral index $n>1$ and arise naturally in the recently proposed hybrid inflationary scenario. An observational upper limit on {\em n} is derived by normalizing the spectrum at the quadrupole scale and considering the possible overproduction of Planck mass relics formed in the final stage of primordial black hole evaporation. In the inflationary Universe with the maximum reheating temperature compatible with the observed quadrupole anisotropy, the upper limit is $n=1.4$, but it is slightly weaker for lower reheat temperatures. This limit applies over 57 decades of mass and is therefore insensitive to cosmic variance and any gravitational wave contribution to the quadrupole anisotropy. It is also independent of the dark matter content of the Universe and therefore the bias parameter. In some circumstances, there may be an extended dust-like phase between the end of inflation and reheating. In this case, primordial black holes form more abundantly and the upper limit is $n=1.3$.