Precision Calculation of Dark Radiation from Spinning Primordial Black Holes and Early Matter Dominated Eras

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 g < MBH < 10 9 g will be probed by CMB Stage 4 experiments.

Exploring Evaporating Primordial Black Holes with Gravitational Waves

“…BH rotation generally increases the emission and favors particle production with larger spin [41,43,68,69]. Detailed numerical analyses [70,71] show that spin-2 graviton emission is significantly enhanced in rotating evaporating BHs, which dominates the resulting copious production of DR when PBHs of 10 9 g mass dominate the energy density and that will affect BBN and cosmic microwave background radiation (CMB) observations. Note that the emitted gravitons correspond to extremely high frequency gravitational waves (GWs), which are undetectable with current or near-future interferometer experiments (e.g.…”

“…Given an initial spectrum of fluctuations one can then find the induced GW spectrum by multiplying with the appropriate kernel [Left] Contributions to ∆N eff from Hawking evaporation production ("PBH decay", blue) taken from Ref. [70], as well as induced GWs (P Φ = 10 −26 in black, P Φ = 10 −28 in gray) for Schwarzschild (a * = 0, solid line) and Kerr (a * = 0.9999, dashed). The 95% C.L.…”

“…The 95% C.L. limits on ∆N eff from CMB (shaded red) are taken from [76] and the 95% limit on BBN from [70], the prospective CMB-S4 sensitivity is shown with horizontal red line [77].…”

“…FIG.1. [Left] Contributions to ∆N eff from Hawking evaporation production ("PBH decay", blue) taken from Ref [70],. as well as induced GWs (P Φ = 10 −26 in black, P Φ = 10 −28 in gray) for Schwarzschild (a * = 0, solid line) and Kerr (a * = 0.9999, dashed).…”

“…The 95% C.L. limits on ∆N eff from CMB (shaded red) are taken from[76] and the 95% limit on BBN from[70], the prospective CMB-S4 sensitivity is shown with horizontal red line[77]. [Right] GW spectral density induced by early isocurvature fluctuations in the PBH reheating scenario in terms of frequency.…”