Martel, Shapiro, and Weinberg (1998) proposed a
possible resolution of the well-known "cosmological constant problem,"
widely viewed as the most serious problem in cosmology today. Though the
evidence is still equivocal, there are persistent hints of a nonzero
cosmological constant corresponding to a vacuum energy density rho_V
which is positive and up to 3 times greater than the present cosmic mass
density rho_0. From the point of view of fundamental quantum physics,
such a value seems absurd. Crude estimates indicate a value of rho_V some
120 orders of magnitude greater than rho_0, and no mechanism has yet
been identified that would make rho_V vanish. A theory which explains
a NONZERO value of rho_V so small as to
be close to rho_0 would be even more peculiar. This is the essence of the
cosmological constant problem. Martel, Shapiro and Weinberg have shown
that an idea common to several current theories (e.g. chaotic inflation),
that the cosmological constant does not have a single, fixed value, but
instead takes a different value in different parts of the universe,
with varying probability, may hold the key to resolving the crisis.
We demonstrated this by an application of a weak form of the anthropic
principle, as follows. In theories in which the cosmological constant takes a
variety of values in different "subuniverses," the probability distribution
of its observed values is conditioned by the requirement that there must be
someone to measure it. This probability is proportional to the fraction of
matter which is destined to condense out of the background into mass
concentrations large enough to form observers. We calculated this "collapsed
fraction" analytically by a simple, pressure-free, spherically symmetric,
nonlinear model for the growth of density fluctuations in a flat universe
with arbitrary value of the cosmological constant, applied in a statistical
way to the observed spectrum of density fluctuations at recombination,
determined using the flat, CDM model with nonzero cosmological constant and the
COBE DMR measurements of microwave background anisotropy. Remarkably enough,
we found that the small, nonzero cosmological constant suggested recently by
several lines of astronomical evidence is a reasonably likely value
to observe, even if there is nothing about the a priori probability
distribution that favors such relatively small values!