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