We now turn our attention to structure formation in the universe.
Actually since the original disappointment of the failure of
classical cosmological tests due to galaxy evolution in 1970s until the
revival of precision cosmology in late 1990s.
This was the main subject of cosmological research.
So here is the problem in the nutshell. We see the dance defluxuations in the
early universe imprinted on the cosmic microbe background photosphere.
They're roughly parts in a million. Today, we see a large-scale structure,
clusters, filaments, voids with density contracts of about 100.
And then, within them there are galaxies whose average density within say half
life radius is about million times larger than the surrounding So how do go from
fluctuation, that there a part in a million, to large scare structure, that
is factor of 100 over dense to galaxy that are, factor million over dense and
that is the job. So we believe that the original
fluctuations came from quantum fluctuations in the early universe that
you know due to fluctuations in the number of density of particles and then
they're inflated through the inflationary era to the large scale structures or are
the seeds of large scale structures. The matter then falls into them, and the
density contrast grows. So the observed thing is, fluctuations in
micro background, is radiation and variations that are coupled before the
recombination, which are parts in a million.
But we also observe, galaxy-like structures at the [UNKNOWN] greater than
6. Those are luminous quasars and Even some
real galaxies, and so we know that at least some little pockets of the universe
have achieved the density contrast which are not the part in a million, but a
million for orders of magnitude, in the time elapsed from the microbackground
release until then is of the order of half a billion years, so this is not an
easy thing to achieve. And the question then is, how do we go
from such small seeds of density fluctuations to the large density
contrast that is observed in the objects that we see.
Well here is a schematic flow chart of what has to happen.
It begins with inflationary physics or very early [UNKNOWN] physics, which is
not directly observable except as consequences of inflation.
But then those fluctuations will grow and we see their imprint in microbackground
even after microbackground is released, they do grow through gravitation and
stability. The dense parts will attract more matter
and become denser. That part is fairly easily understood and
even modeled. It's Newtonian gravity because it's weak
field. But, then gas falls into those potential
wells, gets condensed, dissipates energy as it falls in.
It makes stars, stars dump energy back, and those are very messy processes which
have to be modeled hydrodynamically, and through radiative transfer.
So, there is transitions from relatively simple, elegant, theoretical [UNKNOWN].
Geometry and gravitation into the really messy hydrodynamics radiation physics of
what actually happens to the variance after the recombination.
so let us set the stage for us. In the early universe, we know that it's
very close to the critical matter dominated universe.
Matter or radiation. And so, it's a very simple overall
Friedmann equation. Regardless of what universe will evolve
to later. Early on, its really close to a omega
matter equal 1. And let's look at an over-dense region.
Some were inside that exactly critical universe.
It is essentially like little closed universe of its own.
And initially, of course it expands, but, as you know, since its densities are
greater than critical and surrounding universes are created also, overdense
must be. that means that at some point, it'll have
to turn around and fall back upon itself. So let's just subtract those two
equations. And so that's, that's Friedmann equation
for the difference in density, which we can simply rewrite as follows.
So that's the difference of densities, but really we're looking at the density
contrast. So, let's just divide it by the mean
density, and so we'll call that as the overdense [UNKNOWN] delta, and its
equation is shown here. Here.
Now, since the density is inversely proportional to the scale factor.
This is density of the matter, remember? So it just gets diluted as the cube of
the radius. We see that the density contrast, the
delta, will grow as the first power of the expansion factor, r of t.
And we call that the era of the linear growth of perturbations.
So between any two different redshifts, the change in the contrast will be given
by the ratio of 1 plus redshift or rather the inverse thereof.
So thet's try this from micro background roughly redshift 1000 to say first quasar
roughly at redshift 5 or so. and we find out that the density contrast
should have grown by a couple parts in thousands, whereas it should have been
millions. So we were off by 9 orders of magnitude
and clearly linear treatment does not apply.
The solution to this is in part that, at the time of the micro background, the
fluctuations that we see are those in varions and photons.
But, underlying them are much deeper fluctuations in dark matter, and those
have been growing since the universe became matter-dominated.
So this is another reason why we think that dark matter must exist, because
without it, we would simply not obtain the large-scale structure that we see.
And that's a key idea. That the density fluctuations are
dominated with the dark matter which, as you recall is several times more by
density of regular bariums and those fluctuations grow even before the
micro-background is released. So the fluctuations we see in
micro-background are just little icing on the cake and after that Those variables
can fall into those already preexisting potential wells built by the dark matter.
Next time we will address this process in a little more detail.