1. Announcements Final exam is Monday, May 9, at 7:30 am. –Students with last names A-K go to 225 CB. –Students with last names L-Z go to 300 CB. –All students must bring their ID. The final exam will be cumulative. The final will be 40 questions, 10-15 will be on cosmology, the remainder on material covered earlier in the semester.

2. Cosmology What is the geometry of the Universe? The contents of the Universe Einstein’s greatest blunder Accelerating Universe Dark energy

3. Review Questions Give three pieces of evidence for the Big Bang model.

4. Three pieces of evidence for the Big Bang model Hubble expansion: galaxies are moving away from us with speed proportional to distance. The ratio of Helium to Hydrogen in gas clouds unaffected by stars. The cosmic microwave background: a 2.7 K glow seen in all directions.

5. Cosmic Microwave Background Small fluctuations are due to sound waves at recombination.

6. Temperature variations in the Cosmic Microwave Background (CMB) are observed to be about 0.0003 K. The expected physical size of the hot/cold regions can be calculated.

7. Curvature of the Universe The curvature of the Universe is determined by the density parameter  0 Measurement of CMB fluctuations gives  0 < 1  negative curvature  0 > 1  positive curvature

8. Contents of the Universe Normal matter –Stars –hot gas –anything made of atoms Total is 4% of  C

9. Rotation curve of Milky Way

10. Mass of the Milky Way

11. Dark Matter Dark – it doesn’t produce light (any kind) Does have mass, produces gravity Nature is unknown Most likely it is elementary particles

12. Contents of the Universe Normal matter is 4% of  C Dark matter is 23% of  C Total of normal and dark matter is  M = 0.3 But, we need 100% of  C Remainder, 73%, is dark energy   = 0.7

13. Contents of the Universe

14. Why can't we see radiation produced during the first 300,000 years after the Big Bang? 1.It was absorbed soon after it was emitted. 2.It hasn't reached us yet. 3.It has been deflected by black holes. 4.It passed by our part of the universe a few billion years ago.

15. Einstein and Cosmology After Einstein wrote down the equations for General Relativity, he made a model of the Universe and found that the Universe had to be either expanding or contracting. He introduced a new term, the cosmological constant or , in his equations representing a energy field which could create antigravity to allow a static model. After Hubble found the expansion of the Universe, Einstein called  his greatest blunder.

16. Cosmological Constant Quantum physics predicts that some energy fields that act like . One such field is the one thought to cause the rapid expansion of the Universe during inflation. Another such field appears to be operating today.

17. Matter slows down expansion

19. Accelerating Universe

20. Accelerating universe

21. Accelerating Universe Hubble expansion appears to be accelerating Normal matter cannot cause acceleration, only deceleration of expansion Dark energy is required –may be cosmological constant –may be something else –major current problem in astronomy

22. Review questions How can fluctuations in the cosmic microwave background be used to determine the geometry of the Universe? What are the major components and their fraction of the total mass/energy in the Universe?