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Cosmology

Cosmology. I. Topics. Early Milestones The Expanding Universe Measuring the Expansion. p.364. Early Milestones. 1823 – Heinrich Olbers An infinite universe of infinite age contains infinitely many stars.

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Cosmology

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  1. Cosmology I

  2. Topics • Early Milestones • The Expanding Universe • Measuring the Expansion

  3. p.364

  4. Early Milestones • 1823 – Heinrich Olbers • An infinite universe of infinite age contains infinitely many stars. • Therefore, if you look in any direction in the sky, eventually, your line of sight would intercept the surface of a star.

  5. Early Milestones – II • Olbers’ Paradox • Since every direction leads to a star, the sky would appear to be tightly packed with stars and the sky would always be bright. • So why is the sky dark?

  6. Early Milestones – III • 1848 – Edgar Allan Poe • The universe may be infinitely large but be of finite age. • If so, light has not yet reached us from the most distant stars. • This would create so many dark gaps between the nearest stars that the sky would appear dark.

  7. A Universe of Finite Age

  8. The Age of the Universe • How old is the Universe? • This question is undefined until one specifies • 1) what one means by the age of the universe • 2) how it should be measured; that is, one needs a theory for the age of the universe. This was recognized as long ago as the 1600s, when Bishop James Ussher determined the age of the Universe.

  9. Bishop James Ussher (1581 – 1656)

  10. The Age of the Universe – II • Bishop James Ussher (1581 – 1656) • Bishop Ussher defined and determined the age of the universe thus: • The age of the universe is defined to be the time since its creation (by God). • It is to be measured by adding the periods specified in the Bible, suitably corrected using available astronomical and historical records. • He determined that the universe was created on Sunday October 23, 4004 BC. 

  11. Early Milestones – IV • 1916 – Einstein • His new theory of gravity, called general relativity, made a startling prediction: • The Universe must be either expanding or contracting, that is, the universe must be dynamic. • However, Einstein rejected his original theory in favor of a modified version that described a static universe. He would later describe this as the biggest mistake of his life.

  12. Early Milestones – V • 1924 – Edwin Hubble • Measured the distances to several galaxies and proved that they are very distant. • Made use of the Luminosity-Period relationship of Henrietta Leavitt.

  13. Luminosity-Period Relationship Fig. 18-11, p.372

  14. The Red-Shift • 1929 – Red shift • Drawing on his own observations and those of others, Edwin Hubble discovered that the red shift, z = (lo - le) / le of the light from distant galaxies increases with distance d. le = emitted wavelength lo = observed wavelength

  15. An Expanding Universe • 1929 – Hubble’ Law • Hubble suggested that the red shift is caused by the motion of galaxies away from us. • Moreover, since red shift increases with distance, the further a galaxy is from us the faster it moves. This statement is summarized in Hubble’s Law v = H0 d • H0 is the present-day value of Hubble’s constant H, which is constant throughout space, but not necessarily throughout time.

  16. Fig. 18-4, p.367

  17. Hubble’s Law v = H0 d Fig. 18-5, p.368

  18. d0, t0 L = c (t0 – t1) d1, t1 How Far Is Far ? t0 – t1 is the look-back time d0 = d(t0) is the proper distance between the two galaxies now d1 = d(t1) is the proper distance between the two galaxies then

  19. t1 = past le t0 = now d(t1) a < 1 d0 t2 = future a = 1 d = a d0 lo d(t2) le= a lo a > 1 z= (lo - le) / le 1 + z = 1/a(t) Expansion Without A Center

  20. The Age of the Universe – Today • Hubble’s Law v = H0 d • The Hubble Time d = v t d = H0 d t t = 1/H0 • If H0 = 50 km/s/Mpc then • t ~ 20 billion years.

  21. The Geometry of Space • The Cosmological Principle • On the largest scales, the Universe is isotropic (looks the same in all directions) from every vantage point, at all times. • This implies a universe in which matter and energy are uniformly distributed, that is, a Universe that is homogeneous.

  22. Fig. 18-19b, p.377

  23. The Geometry of Space – I I • Critical Density • Density that allows expansion forever, but only just: rcrit = 3 H02 / (8pG) • WM = rave / rcrit • Three Kinds of Possible Universe (assuming no anti-gravity forces exist) • Flat Universe • Closed Universe • Open Universe

  24. The Geometry of Space – I II • Flat Universe • The geometry of space has zero curvature, just like the geometry of a plane. This geometry arises if the density is exactly equal to the critical density. • In this case, the universe will expand forever with an ever decreasing speed, reaching zero expansion speed in the infinite future.

  25. The Geometry of Space – I V • Closed Universe • The geometry of space has positive curvature like the surface of a sphere. And like the surface of a sphere, the universe would have a finite volume but no boundary. • Positive curvature arises if the density is greater than the critical density. There is enough matter and energy, eventually, to halt the expansion, causing the universe to contract, finally collapsing in the Big Crunch.

  26. An Expanding Closed Universe Fig. 18-9, p.369

  27. The Geometry of Space – V • Open Universe • The geometry of space has negative curvature. • Negative curvature arises if the matter and energy density isless than the critical density. The amount of matter and energy is too low to slow the expansion sufficiently and the universe will expand forever.

  28. Fig. 18-21, p.378

  29. Flat Space Fig. 18-22a, p.379

  30. Positively Curved Space Fig. 18-22b, p.379

  31. Negatively Curved Space Fig. 18-22c, p.379

  32. Positive versus Flat: Angular Size Fig. 18-24a, p.382

  33. Positive versus Flat: Brightness Fig. 18-24b, p.382

  34. Measuring the Expansion • Measuring Using Standard Candles • Type Ia supernovae, which occur a few times per minute somewhere in the known Universe, can be used as standard candles to measure very great distances. • In 1998, two teams – one led by Saul Perlmutter, the other by Brian Schmidt – announced that these supernovae were fainter (and therefore further away) than expected for a decelerating Universe. • The Universe appears not to be slowing down as much as expected and may even be accelerating!

  35. Fig. 18-20, p.377

  36. Fig. 18-27, p.384

  37. Type IA Supernova Light Curves Standard Candles White dwarfs that explode when their mass reaches the Chandrasekhar limit. Fig. 18-28, p.385

  38. To Be Or Not To Be ? Fig. 18-29, p.385

  39. Summary • The Expansion of the Universe • In 1929, Hubble discovered the expansion of the Universe. • Evolution of the Universe • If no anti-gravity effects exist, the fate of the Universe is determined by WM, its density relative to the critical density. • However, distant Type Ia supernovae seem to be further away than expected, which implies that the Universe is not slowing down as much as expected. • If this is confirmed, then some anti-gravity effect is countering the breaking effect of gravity.

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