Kiefer C. Quantum gravity

242 QUANTIZATION OF BLACK HOLES
lg α max
0
-10
-20
1.
2.
4. 5.
7.
3.
6.
5 10 15 20 25
lg M[g]
Fig. 7.5. Strongest constraints on the initial PBH mass fraction. The numbers
correspond to the various entries in Table 7.2.
gives surprisingly strong restrictions (cf. Bringmann et al. 2002). For a scalefree
power spectrum of the form ∝ k n , as it is usually discussed for inflationary
models, one finds restrictions on n that are comparable to the limits obtained
by large-scale observations (anisotropy spectrum of the cosmic microwave background
radiation). Since these restrictions come from observational constraints
referring to much smaller scales, they could constitute an important complementary
test. However, according to present observations of the microwave background,
the actual value for n is too small to give a high-enough rate for PBH
formation to be observable. The only possibility, it seems, is inflationary models
with a distinguished scale (Blais et al. 2003). The ensuing amount of PBHs
could then in principle contribute significantly to the cold dark matter present
in galaxies.
The question whether PBHs really exist in nature has thus not yet been
settled. Their presence would be of an importance that could hardly be overestimated.
They would give the unique opportunity to study the quantum effects of
black holes and could yield the crucial key for the construction of a final theory
of quantum gravity.