Cosmic Structure Formation

Outline

COBE-DMR and CMBR Anisotropies
Cosmic Seeds and the Face of God
Cosmic Seeds and Galaxies

Observed Cosmic Structure in the CMBR

small inhomogeneities are observed in the CMBR from COBE:

anisotropy level is ~ 10^-5

and other smaller angular scale experiments such as HACME (from UCSB):

anisotropy level is also ~ 10^-5

or Saskatoon (Princeton & Penn):

anisotropy level is also ~ 10^-5

It is expected that the full sky looks something like:

At higher angular resolution than COBE-DMR's 7 degrees:

Observed Structure in the Galaxy Distribution

The "Great Wall" is the passing horizontally through these CfA "slice of the Universe" maps

Above is the map of a slice 6 degrees thick, and below is the combination of 6 such slices

The radius of these slices is 15,000 km/sec or z = 0.05

with a Hubble constant of H₀ = 70 km/sec Mpc^-1, this is 210 Mpc = 700 million light years

Note the "fingers of God" pointing at us at the vertex of the slice

These are artifacts of using Hubble's law to get distances

galaxies have "peculiar" velocities due to the gravitational forces from nearby galaxies
these peculiar velocities become very large (> 1,000 km/sec) in dense clusters of galaxies
so, large peculiar velocities lead to distance errors which spread the clusters out along the line of sight.

Note that the typical size of the structures (or voids) is 5,000 km/sec or z = 0.017

or 70 Mpc = 230 million light years
This is close to the full size of the survey!

More recent surveys cover larger volumes of space
Here's the Las Campanas Redshift Survey double "pie diagram"

This is 4 times larger than the CfA survey at 60,000 km/sec or z = 0.20
or 860 Mpc = 2.8 billion light years
note that the largest structures are still at 5,000 km/sec or 70 Mpc

The 2dF Survey goes to the same distance, but plans to get 250,000 galaxies all over the Southern sky

The Sloan survey in the north plans to get 1,000,000 galaxies
the big difficulty is to get all those redshifts

the CfA survey does them 1 at a time, but Sloan and 2dF do 100's at a time with lots of fiber optics cables
Here is a photo of their monster spectrograph on the AAT 4m telescope
Here is a photo of the spectrograph "plate" which is supposed to have optical fibers for 400 spectra at once

Here are some basic facts about the distribution of galaxies at present:

the connection between galaxies and the underlying mass distribution is uncertain

the mass of galaxies is dominated by dark matter - not stars

galaxies may be more clustered than stars

this is called "biasing"
for now, we'll ignore this possibility
it is likely to be only a factor between 1 and 2

the distribution of mass is characterized by the mass density:
the mass density fluctuations are referred to by
on a scale of about 8 Mpc, = 1

it is larger on small scales and smaller on large scales

on scales above about 100 Mpc (330 million light years) drops sharply

This is why the galaxy distribution plots look smooth this scale and larger.

The Growth of Cosmic Structure

How does at last scattering relate to today?

Recall that in the standard picture is related to at last scattering:

Here's a space-time diagram that is supposed to show how this works:

This plot uses "co-moving" coordinates - the coordinates move with the expansion

is the gravitational potential that is proportional to -
We're at the top vertex and the red lines are our past lightcone

we see the CMBR anisotropy only where the red lines intersect the "last scattering surface" which is the shaded region on the bottom

positive => higher density => higher T => positive
positive => stronger gravity => negative

due to gravitational redshift

these 2 effects tend to cancel, but the redshift is stronger

positive regions have negative

because of the rough approximate cancellation (and other factors), we have

~ -10 so
at last scattering ~ 10^-5 => ~ 10^-4

on 8 Mpc scale ~ 1 today

we need something like a factor of 10⁴ in growth

Recall that density perturbations grow due to gravity:

Here are the trajectories of individual particles move in the same kind of space-time diagram:

The fluctuations in the density grow with time

dense regions tend to collapse and become denser

with respect to the average of the Universe
only in the final stages does the collapse overcome the overall expansion

sparse regions don't slow their expansion as much as regions of average density so they appear to grow sparser

When can density perturbations ,, grow?

The Universe must be matter dominated

radiation moves to fast to escape from any perturbation (unless a black hole is forming)

When the Universe is matter dominated (after z = 30,000 or so)
density perturbations in ordinary matter grow like

~ a(t) ~ 1/(1+z) like the scale factor of the Universe
when the universe expands by a factor of 10, a(t) and both grow by a factor of 10.

density perturbations can only grow on scales that are "inside the horizon"

this means scales < ct or so
due to the Universal speed limit, gravity can't really act on larger scales than this

For baryonic matter (i.e. ordinary atoms), density perturbations can't grow until the Universe is transparent.

before then, the radiation pressure pushes the atoms in the opposite direction as gravity does

like sound waves

after last scattering, radiation and baryonic matter don't interact.

This is a big problem:

since last scattering is at z ~ 1000, can only grow to ~ 0.1 by today
with only baryons and a CMBR anisotropy of only ~ 10^-5 , galaxies can never form!

The solution: Dark Matter

With dark matter, starts growing when the density of dark matter becomes larger than the radiation density: z = 30,000 or so
There is no problem to get a factor of 10⁴ in growth
At z = 30,000, the horizon scale is roughly 100 Mpc in comoving coordinates

i.e. the horizon scale then will expand to be about 100 Mpc now
this is why we see the lack of structure on larger scales
larger scales have less time to grow => is smaller on those scales

Where Did the Density Perturbations Come From?

They must be present at the horizon scale at z = 30,000

Did they exist at scales > ct at z > 30,000?

flucuations set up between regions that can't communicate?
inflationary theory says YES!

Or did some physical process set them up on large scales at z = 30,000

It has to work at close to the speed of light
cosmic strongs are one example:

This gives a scenario slightly different than described above.

but is still related to