242 The Quantum Structure of Space and Time
6.3 Prepared Comments
6.3.1 Steven Weinberg
Well, I was asked to talk for ten minutes and I don’t have any positive new ideas
to offer; so 1 am going to make some remarks of the opposite sign.
I have a worry about
the anthropic prediction or argument about the vacuum energy: that anthropic
considerations may not really explain quite why it is as small as it is. If you fix the
fluctuations at early times and suppose they don’t scan and then calculate what is
the average vacuum energy density that would be seen by an astronomer, in any part
of the multiverse, weighting, and here Alan’s point on how to weight things comes
in, but if you do something for want of anything better, you weight the different
subuniverses according to the fraction of baryons that find themselves in galaxies
that are large enough to hold on to heavy elements after the first generation of stars,
then you find that the average density that will be seen by all these astronomers
throughout the multiverse, the vacuum energy density, is about 13 times the energy
density of matter in our universe at the present time, not that that’s a fundamental
unit, but it just happens to be a convenient unit. In fact, experimentally, the
number is not 13, it is 2.3 and you can ask what is the probability of getting a
vacuum energy that small. The answer is: it is about 13%, 13% of all astronomers
weighted the way I described will see a vacuum energy as small as we see it. Well,
that’s not so bad: I mean, 13% I could live with, those are the breaks. But this
hinges on an assumption that, in order to hold on to heavy elements, the size of a
fluctuation in the co-moving radius projected to the present has to be 2 Mpc’s or
greater and the answer is quite sensitive to that: if you reduce it to 1 Mpc, then the
probability goes from 13% down to 7%. This is a difficult astrophysical question
which is beyond my pay grade but, it really is important for astrophysicists to settle
the question of how large fluctuations have to be to hold on to their heavy elements.
And I just wanted to give you that to worry about a little bit.
Now, Alan has talked about the wonderful agreement of theory and observation
for the microwave anisotropy, I could not agree more, it’s wonderful, while we have
been ringing our hands, the real cosmologists have been in hog heaven and, as Alan
pointed out, everything, all the agreement that we see, not only for the microwave
background but also for large scale structure, which continues the curve up to
larger and larger values of L, large than can be reached by studying the microwave
background, all this agreement flows from the assumption that the perturbations
before they reenter the horizon are adiabatic, Gaussian and scale invariant. With
that and just adjusting the overall scale, you fit these curves. So the wonderful
shape of the curves does not really tell you very much about the early universe,
it tells you the perturbations, when they are outside the horizon, are adiabatic,
Gaussian and scale invariant. Now, that’s usually interpreted in terms of a single
scalar field rolling down a potential and the first caution I would like to offer is that