252 The Quantum Structure of Space and Time
the total volume of the parts with n7/nB = we can live only in the parts
with n,/nB - 10-l' [16].
The second such example, which is in fact very similar, is the ratio of the baryonic
matter density to the cold dark matter density, < = PCDM/PB - 5. In the theory
with light axions, ma << eV, the natural value of this ratio would be much
smaller than 0.2, which was considered as a strong evidence that the axions do in
fact have mass ma N - lop5 eV [17]. The resolution of the problem was very
similar to the one mentioned above: In inflationary cosmology with ma << lop5
eV the universe consists of many different exponentially large regions with different
values of <. The prior probability of formation of the region with different fi
after a period of inflation does not depend on <. However, the existence of galaxies
and stars of our type would be much less probable for fi one or two orders of
magnitude greater than its present value. This provides an anthropic explanation
of the presently observed value of pc~~/p~ [18, 191.
One of the most spectacular applications of the anthropic principle is the cos-
mological constant problem. Naively, one could expect vacuum energy to be equal
to the Planck density, PA - 10g4g/cm3, whereas the recent observational data show
that PA N 10-29g/cm3, which is about 0.7 of the total energy density of the universe
PO. Why is it so small but nonzero? Why p~ nearly coincides with PO?
The first anthropic solution to the cosmological constant problem in the context
of inflationary cosmology was proposed in 1984 in [20]. The vacuum energy density
can be a sum of the scalar field potential V(q5) plus the energy of fluxes V(F). I
argued that quantum creation of the universe is not suppressed if it is created at
the Planck energy density, V(q5) + V(F) = 1, in Planck units. Eventually the field
q5 rolls to its minimum at some value 40, and the vacuum energy becomes p~ =
V(q50) + V(F). Since initially V(q5) and V(F) with equal probability could take any
values with V(+)+V(F) = 1, we get a flat probability distribution to find a universe
with a given value of the cosmological constant PA = V(+o)+V(F). Finally, I argued
that life would be possible only for -PO 5 PA 5 PO. This fact, in combination
with inflation, which makes such universes exponentially large, provides a possible
solution to the cosmological constant problem.
In the next couple of years after my work, several other anthropic solutions to
the cosmological constant problem were proposed [21]. All of them took for granted
that life is possible only for -PO 5 p~ 5 PO. The fact that p~ could not be much
smaller than -PO was indeed quite obvious, since such a universe would rapidly
collapse. Meanwhile the constraint p~ 5 po was much less trivial; it was fully
justified only few years later, in a series of papers starting from the famous paper
by Weinberg [22].
I would be able to continue this discussion, describing the constraints on the
amplitude of density perturbations, on the dimensionality of the universe, on the
electron and proton masses, on the expectation value of the Higgs field, etc. What