1. Announcements Observing for the rest of the semester, until December 9 th, will count for the fourth exam. (Tonight may be clear.) 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. The Shape and Fate of the Universe Assumptions in cosmology Curvature of the Universe Fate of the Universe The Big Bang Cosmic microwave background

3. Assumptions in Cosmology Copernican principle: –We do not occupy a special place. –There are no special places. –The universe is homogeneous if viewed at sufficently large scales. –The laws of physics are the same everywhere.

4. How can we test the Copernican principle? Does the Universe look the same in all directions? (Isotropy) Are the spectral lines from atoms the same in distant galaxies? Do the same laws of gravity apply in other galaxies?

5. Implications of the Copernican Principle The average density of matter and energy is the same throughout the Universe. The same Hubble expansion law is seen for all observers anywhere in the Universe. The curvature of the Universe is the same everywhere.

6. Curvature of the Universe The curvature of the Universe is determined by: the density of matter and energy –higher density produces positive curvature the expansion of the Universe –more rapid expansion produces negative curvature

7. Curvature of the Universe The curvature of the Universe is determined by the density parameter  0 Critical density  c = 10 -26 kg/m 3  0 < 1  negative curvature  0 > 1  positive curvature

8. Fate of the Universe

10. Age of the Universe

11. Imagine that the circumference of a circle with a radius of 1000 Mpc was measured to be 5500 Mpc. This would imply that 1.The Universe is flat. 2.The Universe is positively curved and will eventually contract in a big crunch. 3.The Universe is negatively curved and will expand forever.

12. Big Bang Our conclusion that the Universe actually began at some point in time is based on extrapolating back the observed Hubble expansion of galaxies Is there any other evidence?

13. Temperature Temperature is a measure of how fast the atoms in a gas move Hotter  atoms move faster  higher energy density Cooler  atoms move slower  lower energy density Anything will melt if the temperature is high enough

14. Big Bang If the Universe was smaller in the past, but had roughly the same amount of matter and energy, then the density of matter and energy must have been higher in the past.

15. Big Bang

18. First protons and neutrons at about 1 second. Helium nuclei formed at about 100 seconds. Observed ratio of Helium/Hydrogen matches Big Bang prediction. Universe is opaque.

19. Opaque

20. Big Bang At one million years, electrons combine with nuclei and atoms form. Universe becomes transparent.

21. Transparent

22. Cosmic Microwave Background The Universe glows at 2.7 K in every direction.

23. CMB Discovered by Arno Penzias and Robert Wilson in 1960-65 while employed by AT&T’s Bell Labs and attempting to find the source of noise in an antenna used to bounce telephone signals bounced off metallic balloons high in the atmosphere. They won the Nobel prize in 1978.

24. CMB Radiation is a blackbody spectrum originally emitted at 3000 K but red shifted by a factor of 1000.

25. Review Questions Give three pieces of evidence for the Big Bang model. What will happen to the Universe if the density is less than the critical density? A few seconds after the big bang did hydrogen atoms exists? Why or why not?