Cosmological models

Loren Haarsma (lhaarsma@retina.anatomy.upenn.edu)
Mon, 23 Mar 1998 09:52:10 -0500 (EST)

I finally have a spare moment to write some more details about
cosmological modeling (for those of you who are interested...).

Cosmologists who model the "early universe" (the first 300,000
years) use as input data the mass density of the universe, the rate
of expansion, and the standard model of particle physics (including
particle masses, coupling constants of the various forces, etc.)
(There may be some other important inputs, too.)
During this era, photons and matter were in thermal equilibrium and
almost uniformly distributed. At about 300,000 years, the universe
cooled enough so that electrons could remain bound in atoms, so matter
and all those photons could effectively "decouple." Most of the photons
never interacted with matter again. They red-shifted as the universe
expanded, and are now the cosmic microwave background. The existence
of the CMB is the data that really convinced cosmologists of the Big Bang
(instead of various steady-state models).

Three other interesting predictions of big bang models are (1) the
ratio of photons to particles in the universe, (2) the cosmological
abundance ratios of hydrogen, deuterium, and helium, and (3) small-
scale fluctuations in the CMB. The first two can be predicted with a
high degree of accuracy, and have been confirmed to within fairly tight
error bars. However, the size of the small-scale fluctuations in the
CMB is only very loosely predicted. Different models by different
inflationary cosmologists produce a wide range of predicted
fluctuation sizes, while still fitting all the other data. So the
"error bars" -- the level of uncertainty -- on this particular
parameter were quite large. (many orders of magnitude!)

(Sidenote: some major sources of uncertainty in the predictions of
models like these are (1) uncertainty in the initial conditions, which
propagate through to the final conditions; (2) estimates of the size of
the effects of "secondary processes" which the model neglects in favor
of concentrating its calculations on dominant physical processes; and
of course the infamous (3) round-off errors, which can propagate
through the calculations.)

Cosmologists working on large-scale structure formation in the "later
universe" typically start their models at around 300,000 years,
using as input the predicted conditions from the "early universe"
models, and try to model the distribution of matter
into galaxies, clusters, and super-clusters that we see today.
One of the most crucial pieces of information for large-scale structure
formation is the size of those density fluctuations in the
distribution of matter at 300,000 years. (The density fluctuations
in the CMB give an accurate measure of the density fluctuations of
matter at that same time, since the photons and matter were in thermal
equilibrium up until then.) Unfortunately for structure theorists,
that crucial piece of information was one thing they couldn't get from
the models of the earlier universe -- at least, not within any useful
limits.

Even before any fluctuations in the CMB were measured, structure-theorists
knew that those fluctuations had to fall into a certain range (the range
was about 2 orders of magnitude in size). If the fluctuations were too
large, the universe would become much clumpier than it is now; if the
fluctuations were too small, structure couldn't form.

Then the COBE satellite measured fluctuations in the CMB, and the size
of the fluctuations were within the estimates of structure-theorists
models (and, of course, within the very large uncertainty of inflation
theorists' models). Now that structure theorists have actual data on those
fluctuation sizes nailed down much more accurately, they can use that
data to improve their models. With a few further improvements in the
COBE data, and a few further improvements in the calculational
abilities of their models, they should soon be able to make some
predictions that they hadn't been able to before. For example, models
which have slightly different cosmological constants, or different
amounts of uniformly distributed weakly interacting dark matter
("WIMPS"), or different amounts of "clumpy" ordinary (dark) matter,
will start to make different predictions about the expected arrangement
of large-scale structure today --- predictions which can be compared
with observational data. So by using the COBE data (which is
consistent with, but much more tightly constrained than the predictions
of earlier models) as initial conditions, structure-theorists can make
better predictions for new observations.

Loren Haarsma