Cosmology 243this outcome is actually much more robust than that and much more generic and
so that there isn’t that much reason to believe in this very simple picture.
First of all, that the perturbations are adiabatic. By the way, in practice, as
far as the microwave background is concerned, that means that bp/(p +p) (p being
the energy density and p being the pressure) is the same for the cold dark matter
and the photon-baryon plasma, and that is verified to a fair degree of accuracy,
although is is not very accurate right now. Well, that is extremely easy to achieve:
it’s automatic if you have a single scalar field rolling slowly down a potential; it’s
not automatic if you have many scalar fields, as you might expect, but if after
inflation all these scalar fields dump their energy into a heat bath and if at that
time, because baryon-number has not yet been generated, there were no non zero
conserved quantum numbers, then of course automatically the perturbations must
be adiabatic; that’s almost trivial. What is a little bit less trivial is that later
on, when the cold dark matter and then the neutrinos decouple from the photon-
baryon plasma, the perturbations remain adiabatic. So that, it is by no means true
that if you have many scalar fields you expect non adiabatic perturbations to be
observed at the present time. Now, it is possible that you can get non adiabatic
Perturbations, there are the so called curvaton models, where you carefully arrange
that some of the scalar fields that were present during inflation do not dump their
energy into the heat bath but survive for some reason and these provide a model for
non adiabatic perturbations. I think that the generic case is that you get adiabatic
perturbations. That is true even if you have things much weirder than scalar fields:
as long as after inflation you have a heat bath with no non zero conserved quantum
numbers, then, even later when you no longer have local thermal equilibrium, you
still have purely adiabatic perturbations.
That they are Gaussian, well, that follows from the fact that the perturbations
are small, we know that experimentally, and that there was a time (this is true of a
lot of theories although not all theories) in the very very early universe, when the
physical wave number was large compared to the expansion rate, that the fields be-
haved like free fields. It’s easy to arrange theories of many kinds including multiple
scalar field theories in which that is true and if it is true, then you get Gaussian
perturbations.
Scale invariance? Well, there are lots of theories that give you scale invariance.
I made that remark at a meeting in Santa Barbara and Andrei Linde challenged
me to thing of others. Of course, one example is multiple scalar fields all rolling
slowly down a potential, but I could not really come up with any alternative but,
Neal Turok here, just the other day, pointed out that in the oscillating or bouncing
cosmology that he was suggesting you do get scale invariant perturbations. And
scale invariance after all, scale invariant perturbations are pretty ubiquitous in
nature, communications engineers call them l/f noise and they are used to l/f
noise, even though it has nothing to do with inflation.
So, I would say that what you really need in order to settle these questions and