Astr 1050     Wed., Nov. 20, 2002
   Today:  Chapter 15, Cosmology
              Leonids reports
A great webpage tutorial on cosmology.  Recommended! http://www.astro.ucla.edu/~wright/cosmolog.htm

Chapter 15: Cosmology
Olber’s paradox
The Hubble Expansion – review+
The Big Bang
Refining the Big Bang
Details of the Big Bang
General Relativity
Cosmological Constant
Origin of Structure

Olber’s Paradox:
Why is the night sky dark?
If we are in a forest which extends far enough then
In any direction we will just be looking at the trunk of some
tree.

Olber’s Paradox:
Why is the night sky dark?
If we are in a universe which extends far enough then
In any direction we will just be looking at the surface of some star.

Olber’s Paradox:  Answer
It could be that the Universe doesn’t extend far enough –
but that doesn’t seem to be the right answer
The finite age of the universe limits how far we can see:
If it has age T, we can only see out as far as d=c
´T
The light from farther stars hasn’t had time to reach us yet

Basic Cosmology Assumptions
Homogeneity – matter is uniformly spread across the universe on large scales
Isotropy – the universe looks the same in all directions, again strictly true on large scales
Universality – laws of physics apply everywhere in the universe (being challenged!)
These lead to the “cosmological principle” which says that any observer in any galaxy in the universe should see essentially the same features of the universe.

The Hubble Law and the Age of the Universe
Ho = 72 ±8 km/s/Mpc

Hubble Law:  Everyone sees same expansion

Universal Expansion: Balloon Analogy
Simulation of a “closed” spherical universe expanding:
http://www.astro.ucla.edu/~wright/Balloon2.html
The points here are that
Expansion looks the same from each galaxy
There is no “center” of the universe
Galaxies do not expand
Photons are redshifted because space itself is expanding

Early History of Universe?
Run time “backwards” to understand
Density goes up as expansion “reverses”
Temperature goes up as material is compressed
The early universe was very hot and dense.
This is the essence of the “Big Bang” model, which has numerous testable predictions.

Consider a molecular H2 , He gas as it gets hotter
H2 molecules break apart into H atoms
H atoms loose their electrons
He atoms lose their electrons
He nuclei break apart into protons, neutrons
Protons and neutrons break apart into quarks
More exotic massive unstable particles are created
You get more and shorter wavelength photons
You get a quasi-equilibrium between photons and matter
               High energy photons Û (particles + antiparticles)

Critical points with time running forward
10-45 sec Quantum gravity?  Physics not understood
10-34 sec 1026 K Nuclear strong force/electro weak force separate
(inflation, matter/antimatter asymmetry)
  10-7 sec 1014 K Protons, AntiprotonsÛphotons
  10-4 sec 1012 K Number of protons frozen
    4   sec            1010 K                  Number of electrons frozen
    2   min Deuterium nuclei begins to survive
    3   min 109  K Helium nuclei begin to survive
  30   min           108  K                     T, r too low for more nuclear reactions
(frozen number of D, He -- critical prediction)
300,000 yr 104  K Neutral H atoms begin to survive
(frozen number of photons – critical prediction)
 1 billion yr Galaxies begin to form
13 billion yr Present time

First prediction from Big Bang model:
Cosmic Background Radiation
Look out (and back in time) to place  where H became neutral
Beyond that the high density ionized H forms an opaque “wall”
Originally 3000 K blackbody radiation
The material that emitted it was moving away from us at extreme speed
That v produces extreme redshift (z=1000), so photons all appear much redder, so T appears cooler
With red shift, get 2.7 K Planck blackbody
Should be same in all directions

Cosmic Microwave Background Observations
First detected by Wilson and Penzias in 1960’s
Serendipitous detection – thought is was noise in their radio telescope but couldn’t find cause.  Only later heard of theoretical predictions
Best spectrum observed by COBE satellite
Red curve is theoretical prediction
43 Observed data points plotted there
error bars so small they are covered by curve.
it is covered by curve.
Isotropy also measured by COBE
T varies by less than 0.01 K across sky
Small “dipole” anisotropy seen
Blue = 2.721    Red = 2.729
Caused by motion of Milky Way falling towards the Virgo supercluster.

Second prediction from Big Bang Model:
Abundance of the light elements
Big Bang Nucleosynthesis
T, r both high enough at start to fuse protons into heavier elements
T, r  both dropping quickly so only have time enough to fuse a certain amount.
Simple models of expansion predict 25% abundance He
25% is the amount of He observed
Abundance of 2H, 3He, 7Li depends on rnormal matter
Suggests rnormal matter is only 5% of rcritical
But we need to also consider “dark matter” and its gravity

Main Tests of the Big Bang
Hubble Expansion (not a test really, inspiration)
Cosmic Microwave Background
Abundance of light elements

Refinements of Big Bang Still Being Tested
Possible “cosmological constant”
Very early history:
particle/antiparticle asymmetry
“inflation” -- Details of very early very rapid expansion
small r, T fluctuations which lead to galaxies

Will the expansion stop?
Is there enough gravity (enough mass) to stop expansion?
Consider an simple model as first step  (full model gives same answer)
Treat universe as having center
Assume only Newtonian Gravity applies
Does a given shell of matter have escape velocity?  Is v > vesc ?

General Relativistic Description
What we call “gravity” is really bending of our 3-d space in some higher dimension.
Bending, or “curvature of space” is caused by presence of mass.
More mass implies more bending.
If bending is enough, space closes back on itself, 
just like 2-d surface of earth is bent enough in 3rd dimension
to close back on itself.

Mass and the Curvature of Space
First consider case with little mass (little curvature)
Ant (in 2-d world) can move in straight line from point A to point B.
Add mass to create curvature in extra dimension invisible to the ant.
   In trying to go from point A to
   point B, fastest path is curved one
   which avoids the deepest part of the
   well.
  Ant will be delayed by the extra
  motion in the hidden third
  dimension.
Both effects verified in sending photons past the sun:
  Bending of starlight during solar eclipse
  Delay in signals from spacecraft on
  opposite side of the sun

How to test the amount of curvature
Measure the circumference of a circle as you get farther and farther from the origin:
Does it go up as expected from (2 p R)?
It goes up slower in a positively curved world.

How high is the density?
Not nearly enough normal matter to provide critical density
We keep seeing effects of gravity from “dark matter”
Higher rotation speeds in our own galaxy
Higher relative velocities of galaxies in clusters
Rate at which matter clumps together to form galaxy clusters
Gravitational lensing from galaxies, clusters
May be 10 to 100 times as much “dark matter” as visible matter
What might make up the “dark matter”?  Possibilities include
MACHOs (massive compact halo objects) http://www.astro.ucla.edu/~wright/microlensing.html
but 2H, Li, Be abundance suggest no more than 5% can be “baryonic”
WIMPs (weakly interacting massive particles) predicted by some GUT’s
Mass of neutrinos
Mass equivalent of “cosmological constant” energy

Refining the Big Bang
Flatness Problem – why so close to a critical universe?
Horizon Problem – why is background all same T?
SOLVED BY AN “INFLATIONARY UNIVERSE”
“Grand Unified Theories” of combined Gravity/Weak/Electric/Nuclear forces predict very rapid expansion at very early time:  “inflation”
When inflation ends, all matter moving away with v=vescape  (flat universe – curvature forced to zero)
Also solves horizon problem – everything was in causal contact

Implications of Slowing Expansion Rate
Our calculation of age T=1/Ho = 13.6 billion years assumed constant rate
Gravity should slow the expansion rate over time
If density is high enough, expansion should turn around
If expansion was faster in past, it took less time to get to present size
For “Flat” universe  T = 2/3 * (1/Ho) = 9.3 billion years
contradiction with other ages if T is too small

Is the expansion rate slowing?
Look “into the past” to see if expansion rate was faster in early history.
To “look into the past”  look very far away:
Find “Ho” for very distant objects, compare that to “Ho” for closer objects
Remember – we found Ho by plotting velocity (vr) vs. distance
We found velocity vr from the red shift (z)
We found distance by measuring apparent magnitude (mv)
of known brightness objects
We can test for changing Ho by measuring mv vs. z

Measuring deceleration using supernovae
Plot of mv  vs. z   is really a plot of distance vs. velocity
If faint (Þdistant Þearlier) objects show slightly higher z
than expected from extrapolation based on nearby (present day) objects,
then expansion rate was faster in the past and has been decelerating
Surprise results from 1998 indeed do suggest accelerating expansion
May be due to “cosmological constant” proposed by Einstein
AKA “Dark energy” or “Quintessence”

“Cosmological constant”
General Relativity allows a repulsive term
Einstein proposed it to allow “steady state” universe
He decided it wasn’t needed after Hubble Law discovered
Is the acceleration right?
Could it be observational effect – dust dims distant supernova?
Could it be evolution effect – supernova were fainter in the past?
So far the results seem to stand up
Still being determined:  1)  density, 2) cosmological constant
With cosmological constant included, can have a “flat universe” even with acceleration.
Given “repulsion” need to use relativistic “geometrical” definition of flatness, not the escape argument one given earlier.
Energy (and equivalent mass) from cosmological constant may provide density needed to produce flat universe.

Tests using
 the Origin of Structure
Original “clumpiness” is a “blown up” version of the small fluctuations in density present early in the big bang and seen in the background radiation.
We can compare the structure implied to that expected from the “Grand Unification Theories”
Rate at which clumpiness grows depends on density of universe
Amount of clumpiness seems consistent with “flat universe” density
That means you need dark matter to make clumpiness grow fast enough

Acoustic Peaks in Background

Cosmology
 as a testing ground for physics
Extremely high energies and densities in early Big Bang test “Grand Unification Theories” which combine rules for forces due to gravity, weak nuclear force, electric force, strong nuclear force
Extremely large masses, distances, times, test
General Theory of Relativity

Chapter 15: Cosmology
The Hubble Expansion – review+
Olber’s paradox
The Big Bang
Refining the Big Bang
Details of the Big Bang
General Relativity
Cosmological Constant
Origin of Structure