1. The Fate of the Universe

2. The fate depends on the rate of expansion and the density Density greater than critical value – gravity will halt expansion Density less than or equal to the critical value – gravity will not stop expansion

3. Critical density 1 to 2 × 10 -23 g/cm 3 Anything with a density above the critical value will stop the expansion of spacetime.

4. Discussion How would a different expansion rate change Hubble’s plot? That is, how would the distance vs. the recessional velocity graph change if the universe were expanding at twice or ½ the measured value of 70 km/sec/Mpc?

6. Discussion If the expansion of the universe is constant with time, the Hubble plot will be a straight line out to the highest redshifts. What does the Hubble plot look like if the expansion of the universe slows with time? How about if it speeds up over time.

8. Supernova type Ia All have about the same peak luminosity Make good standard candles

9. Discussion If the expansion of the universe is slowing, the expansion rate was greater in the past (at high redshift) than it is today. Will high-redshift galaxies be closer or farther away than we think if we assume a constant expansion rate.

10. With a greater expansion rate in the past, we will think that a given redshift is farther away from us than it actually is.

11. Discussion If the expansion of the universe is slowing, the expansion rate was greater in the past (at high redshift) than it is today. Will high-redshift supernovae be brighter or fainter than we would expect using the present day Hubble constant?

12. We think high redshift supernovae are farther away than they actually are they will appear brighter than we expect

15. Accelerating Supernovae data at high redshift are fainter than we expect the expansion rate of the universe was slower in the past. The expansion rate is increasing with time.

16. Discussion Maybe the rate of expansion is not increasing with time. What else might make supernovae at large redshift dimmer than low redshift supernovae?

17. Discussion Perhaps this is just the effect of dust between us and the distant supernovae, the dust would make them appear dimmer even though they aren’t really farther away. What observations could you do to eliminate this possible explanation?

18. No reddening They do not appear to be reddened by dust.

19. Cosmological constant is back! The cosmological constant introduced by Einstein can be thought of as anti-gravity or a repulsive force pushing the galaxies apart. Some researchers are now referring to this as “dark energy.”

20. Discussion Because mass and energy are the same, this means that dark matter and dark energy are the same right? What is the difference?

21. Universe may not expand forever We know nothing about what dark energy is or how it works Right now, it appears the dark energy is due to a cosmological constant, i.e. constant acceleration over the observable universe

22. Discussion If all the galaxies are getting farther away, what does this tell you about the universe in the past?

23. Discussion What happens when you compress something?

24. Discussion What do you expect to observe from a hot dense gas?

25. Discussion What happens to this blackbody radiation as the universe expands?

27. The cosmic microwave background radiation (CMBR) The universe is filled with microwave radiation that matches a blackbody curve with a temperature of 2.725 K.

30. The universe started from an extremely dense, hot phase from which it expanded in an event termed the “Big Bang.” The Big Bang is an explosion of space and time, not an explosion in space at a time. The hot Big Bang

31. Discussion Where did the Big Bang take place?

32. Discussion What happened before the Big Bang?

33. The isotropy of the CMBR The temperature of the CMBR is the same in all directions. Although is does vary by 0.0033 K in opposite directions, this is interpreted as the Earth’s motion relative to the Universe.

36. If we remove our motion of 620 km/sec in the direction of the local supercluster of galaxies, we find the CMBR temperature varies by less than 1 part in 10,000. In order to be the same temperature, each part of the sky must have been in thermal contact with every other part of the sky.

37. The horizon problem We can see about 14 billion light years in every direction.

39. Inflation An early phase of exponential expansion lasted only 10 -24 sec – Universe expanded by a factor of 10 50. The space between bits of matter expanded faster than the speed of light.

41. The curvature of spacetime Matter and energy warp spacetime

42. Geometry of Spacetime Two parallel lines remain parallel, never getting farther apart of closer together. The sum of the angles in a triangle is 180 degrees.

43. Types of curvature Positive curvature – a closed universe – one the will collapse Negative curvature – an open universe – one that will expand forever Flat – an open universe with density equal to the critical density

44. Positively curved spacetime

45. Negatively curved spacetime

46. Flat spacetime

47. Boundaries and Infinities An open Universe is infinite in space or has no edge A closed Universe in finite but need not be bounded by an edge – think surface of a sphere

48. Discussion How could we determine whether or not the Universe as a whole is negatively curved, flat or positively curved? Adding up the matter is too hard because of the all the dark matter.

49. Discussion How does angular size change with distance?

51. Discussion If all galaxies were exactly the same size, how would they appear as you get farther and farther away in a flat universe, a negatively curved open universe and a positively curved closed universe? Think about what happens to parallel lines in the different curved spaces.

52. If the universe is positively curved or closed, the galaxies will appear to be bigger than you would expect as you go to higher redshifts. Parallel lines converge. If the universe is negatively curved or open, galaxies will appear to be smaller than you expect as you go to higher redshifts. Parallel lines diverge.

53. This doesn’t work! Galaxies are not all the same size. But, the cosmic microwave background radiation is not perfectly smooth either!

54. Creation of Structure A perfectly homogeneous (same everywhere) and isotropic (same in all directions) CMBR forms no galaxies Over-densities of matter collapsed under gravity to form the galaxies and clusters of galaxies.

55. The Jeans length When the universe emitted the CMBR it was about 3000 K, at this temperature we can calculate how big a gas cloud needs to be to collapse under it own weight. This is known as the Jeans length and at the redshift of the CMBR is about one degree in angular size and about the mass of a typical globular cluster.

57. Hot spots As the gas collapses, it heats up and these appear as hot spots in the CMBR.

60. The universe is flat! The universe appears to contain no curvature on large scales. Euclidean geometry holds over large distances. Its expansion will continue forever. That is, as long as the “dark energy” remains well behaved.

61. The flatness problem If the universe is currently flat, it had to be flat to within 50 decimal places before recombination.

62. If the universe had a slight positive curvature, it would have already collapsed in a “Big Crunch.” If the universe had a slight negative curvature, it would have expanded more quickly early on and matter would not have been able to gravitationally collapse. There would be no galaxies, stars or planets.

63. The anthropic principle The universe had to be exactly flat or we wouldn’t be here to observe it!