1. Mini Review: Ocam’s Razor: Start out with simplest assumptions Hot Big Bang, Expanding Universe: Only baryonic matter => CMB existence, universe old and large and expanding

2. CMB too smooth Add non-baryonic matter Galaxies seen early (high 1+z) => CDM First Peak in CMB indicates universe flat IF we put in model of initial fluctuations as adiabatic.  t = 1, k = 0 Second and Third peaks of CMB fit nicely with First peak and adiabatic model, but need MAP data to be sure

3. SNe says from a measure of the geometry of the universe versus time => Accelerating Universe => Dark Energy Clusters of galaxies say  m With CMB  t =1, =>   > 0.6, => Dark Energy Dark Energy is the “dark side” of physics

4. Ways to overcome “dark side” Assume SNe wrong Assume Clusters wrong Assume other new physics (e.g. iso-curvature) in “early” = about 10 -30 sec after BB rather than adiabatic fluctuations => In this case First peak doesn’t require  t =1, k = 0 flat in this case. First Peak in CMB looks so solid need new interpretation for a model with no Dark Energy. Cluster and SNe observations alone are less solid.

5. In “early” Universe, “any goes’ so to a few, iso- curvature more appealing than adiabatic First, Second and Third peaks are likely to be verified by MAP A very neat confirmation of adiabatic initial fluctuations Status quo is very likely to be upheld => Our “final answer” is Dark Energy, CDM, the Universe is “flat” but the expansion rate of the Universe is increasing

6. CMB peak plotplot CMB smoothness map

8. End mini-Review, back to clusters

9. Use hot (100 million K) gas. Most light comes out in X-rays. Some of missing mass was found, but not enough => confirmation of non-baryonic dark matter Second method:

10. Optical X-ray False color No color

11. Concept of escape velocity: If an object is moving fast enough the object will escape the pull of gravity of that system. => (1/2)mv 2 > GMm/R m = mass of escaping object v = velocity of escaping object M = mass of retaining object, R = distance from center to center

12. Atom mass is m (assumed) Cluster mass is M => Measure T of gas Relate T to v (simple theory) Derive M! Derived M agrees with galaxy velocity method

13. Bottom Line from first 2 methods: Gas mass =3-5 times total galaxy mass Total directly detected baryonic matter (galaxies plus hot gas) mass still about 10 (closer to 8) times too low! => Wouldn’t hurt to check another way OK check one more way! => “Gravitational lensing”

14. Gravitational Lensing Magnifies and distorts images

15. Gravitational Lensing 4-d surface is distorted by local mass concentration light travels on the surface light path is deflected when traveling close to the body Black hole

16. Gravitational Lensing Cont. Gives rise to “beautiful effects” Core of the Cluster called A2218 Arc-like structures caused by grav. lensing of the mass in the cluster

17. Grav. Lensing Derive a cluster mass again! Agrees with other methods

18. Number of clusters there are per unit volume lower bound on the  m ! = about 0.1- 0.2 ! We will assume 0.1

19. Models of how clusters form and evolve yield total  m

20. Model of Cluster formation and  m Universe is expanding Density falls => Total mass in a cluster radius is less than cluster mass. => Can’t form any more clusters then.

21. Prediction: If we see a “steep” (factor of 2) in number of clusters per unit volume as go from z = 0.1 to z =1, then  m > 0.7 See shallow change (less than factor of 1.2), then  m < 0.4 See shallow change =>  m < 0.4, all fits!

22. No. of clusters per unit volume z Age of universe Clusters are no longer able to form as the universe is not dense enough: High  m Low  m

23. Clusters have problems also Just measuring the mass is difficult:=>

24. Velocity of galaxy measurement assumes you know all the galaxies are in the clusters and how they are moving. And, where do clusters end (in radius), anyway? Gas mass measurements based on possibly false assumption of stable situation. Our cluster counts could be wrong Our model for relating  m to number of clusters per unit volume with age of universe could be wrong