Abstract
We present precision calculations of dark radiation in the form of gravitons coming from Hawking evaporation of spinning primordial black holes (PBHs) in the early Universe. Our calculation incorporates a careful treatment of extended spin distributions of a population of PBHs, the PBH reheating temperature, and the number of relativistic degrees of freedom. We compare our precision results with those existing in the literature, and show constraints on PBHs from current bounds on dark radiation from BBN and the CMB, as well as the projected sensitivity of CMB Stage 4 experiments. As an application, we consider the case of PBHs formed during an early matter-dominated era (EMDE). We calculate graviton production from various PBH spin distributions pertinent to EMDEs, and find that PBHs in the entire mass range up to $10^9\,$g will be constrained by measurements from CMB Stage 4 experiments, assuming PBHs come to dominate the Universe prior to Hawking evaporation. We also find that for PBHs with monochromatic spins $a^*>0.81$, all PBH masses in the range $10^{-1}\,{\rm g} < M_{\rm BH} <10^9\,$g will be probed by CMB Stage 4 experiments.
Highlights
Black hole evaporation via the emission of Hawking radiation is a well-established phenomenon [1,2], with recent work toward precisely characterizing the Hawking radiation yields of relevant particles and the time evolution of the population of black holes (e.g., Ref. [3])
Following the spin distributions used in Ref. [14] as benchmark examples, we find that Primordial black holes (PBHs) formed during an early matter-dominated era (EMDE) with a spin distribution due to the first-order effect are constrained by current cosmic microwave background (CMB) bounds on ΔNeff in the mass range 108–109 g; they are completely constrained in the mass range 10−1–109 g by projections of CMB Stage 4 experiments
The fact that PBHs formed during an EMDE that evaporate before big bang nucleosynthesis (BBN) will be completely probed by ΔNeff measurements from CMB Stage 4 experiments is the main result of our work
Summary
Black hole evaporation via the emission of Hawking radiation is a well-established phenomenon [1,2], with recent work toward precisely characterizing the Hawking radiation yields of relevant particles and the time evolution of the population of black holes (e.g., Ref. [3]). The fact that PBHs formed during an EMDE that evaporate before BBN will be completely probed by ΔNeff measurements from CMB Stage 4 experiments is the main result of our work. This happens because PBHs formed during an EMDE are endowed with significant spin, which enhances their production of gravitons during evaporation. In terms of the modulus sector, our result is that for a variety of PBH spin distributions and fractions β of the total energy density of the Universe that is constituted by PBHs at formation time during an EMDE, moduli with masses larger than approximately 108 GeV will be constrained by CMB Stage 4 experiments (Fig. 8).
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