Kiefer C. Quantum gravity

OUTLOOK 325
observable universe were collected into a single gigantic black hole. This entropy
would be (in units of k B )about10 123 , which is exceedingly more than the observed
entropy of about 10 88 . The ‘probability’ for our universe would then be
about exp(10 88 )/ exp(10 123 ), which is about exp(−10 123 ). From the anthropic
principle alone one would not need such a special universe. As for the cosmological
constant, for example, one could imagine its calculation from a fundamental
theory. Taking the presently observed value for Λ, one can construct a mass
according to
( 2 Λ 1/2 ) 1/3
≈ 15 MeV , (10.46)
G
which in elementary particle physics is not an unusally big or small value. The
observed value of Λ could thus emerge together with medium-size particle mass
scales.
Since fundamental theories are expected to contain only one dimensionful
parameter, low-energy constants emerge from fundamental quantum fields. An
important example in string theory (Chapter 9) is the dilaton field from which
one can calculate the gravitational constant. In order that these fields mimic
physical constants, two conditions have to be satisfied. First, decoherence must
be effective in order to guarantee a classical behaviour of the field. Second, this
‘classical’ field must then be approximately constant in large-enough space–time
regions, within the limits given by experimental data. The field may still vary
over large times or large spatial regions and thus mimic a ‘time- or space-varying
constant’; cf. Uzan (2003).
The last word on any physical theory has to be spoken by experiment (observation).
Apart from the possible determination of low-energy constants and
their dependence on space and time, what could be the main tests of quantum
gravity?
1. Black-hole evaporation: A key test would be the final evaporation phase of
a black hole. For this one would need to observe primordial black holes; see
Section 7.7. As we have discussed there, these are black holes that are not
the end result of stellar collapse, but which can result from strong density
perturbations in the early universe. In the context of inflation, their initial
mass can be as small as 1 g. Primordial black holes with initial mass of
about 5×10 14 g would evaporate at the present age of the universe. Unfortunately,
no such object has yet been observed. Especially promising may
be models of inflationary cosmology with a distinguished scale (Bringmann
et al. 2002).
2. Cosmology: Quantum aspects of the gravitational field may be observed
in the anisotropy spectrum of the cosmic microwave background. First,
future experiments may be able to see the contribution of the gravitons
generated in the early universe. This important effect was already emphasized
by Starobinsky (1979). The production of gravitons by the cosmological
evolution would be an effect of linear quantum gravity. Second,