Constraints on the mass spectrum of primordial black holes and braneworld parameters from the high-energy diffuse photon background
Constraints on the mass spectrum of primordial black holes and braneworld parameters from the high-energy diffuse photon background
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高能扩散光子背景对原初黑洞质谱和膜世界参数的约束
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发表时间：
2003
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通讯作者：
Katsuhiko Sato
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作者：
Y. Sendouda;S. Nagataki;Katsuhiko Sato
本文研究了Randall-Sundrum II型膜世界中蒸发的原初黑洞（PBH）发射的高能漫射光子的光谱形状。在他们的膜世界假设中，小PBH的性质与普通四维情况相比有了很大的改变，原因有两个。(i)下降霍金温度，相当于延长寿命的个人PBH由于时空拓扑结构的变化和（ii）的有效增加的PBH的总量所造成的吸积在辐射为主的时代，膜高能量阶段的最早的一部分。从预期的光谱形状和它的依赖braneworld参数的研究，我们得到了两个定性的不同的可能性的约束braneworld PBH的观测扩散高能光子背景。如果在高能量阶段的吸积效率超过一个临界值，额外的维度的存在给出了一个更严格的上限比4D的情况下的PBH的丰度和一个小的长度尺度的额外的维度是有利的。相反，在临界吸积效率以下的情况下，我们发现对PBH丰度的约束可以放宽几个数量级，以换取大额外维的存在;它的大小甚至可以限制在10^{19}以上的区域中。乘以四维普朗克尺度，假设PBH的静止质量能量密度相对于辐射的能量密度实际上大于10^{-27}（4D上限）在其形成时间。上述分析结果也得到了数值验证，并明确给出了膜世界参数和PBH丰度的允许范围。
We investigate the spectral shape of a high-energy diffuse photon emitted by evaporating primordial black holes (PBHs) in the Randall-Sundrum type II (RS2) braneworld. In their braneworld scenario, the nature of small PBHs is drastically modified from the ordinary four-dimensional case for the following two reasons. (i) dropping Hawking temperature, which equivalently lengthens the lifetime of the individual PBH due to the change of space-time topology and (ii) the effective increase of the total amount of PBHs caused by accretion during the earliest part of the radiation-dominated epoch, the brane high-energy phase. From studies of the expected spectral shape and its dependence on braneworld parameters, we obtain two qualitatively distinctive possibilities of constraints on the braneworld PBHs from the observations of diffuse high-energy photon background. If the efficiency of accretion in the high-energy phase exceeds a critical value, the existence of the extra dimension gives a more stringent upper bound on the abundance of PBHs than the 4D case and a small length scale for the extra dimension is favored. On the contrary, in the case below the critical accretion efficiency, we find that the constraint on the PBH abundance can be relaxed by a few orders of magnitude in exchange for the existence of the large extra dimension; its size may be even bounded in the region above 10^{19} times 4D Planck length scale provided the rest mass energy density of the PBHs relative to energy density of radiation is actually larger than 10^{-27} (4D upper bound) at their formation time. The above analytical studies are also confirmed numerically, and an allowed region for braneworld parameters and PBH abundance is clearly obtained.