Cosmology

1. 1 2015 Nov Cosmology Dr. Bill Pezzaglia

2. 2 Cosmology The UNIVERSE: • Eternal, infinite, unchanging? Or • Had a beginning, and may end?

3. 3 Cosmology: What is it? Cosmos vs Chaos Meaning of Cosmology

4. 4 Cosmology • Static Cosmology • Expanding Universe • Decelerating Universe

5. 5 A. Static Cosmology • The Infinite Universe • Olber’s Paradox • The Finite Universe

6. 6 A.1a Static Cosmology Copernicus Cosmological Principle: • Universe is isotropic & Homogeneous • No Preferred Center(leads to conservation of momentum) • Verified by Hubble’s Galaxy Survey

7. 7 A.1b Newtonian Cosmology Newton proposed that the universe must be infinite to be balanced; a finite universe would collapse due to gravity But: • 1823 Olber shows universe is not infinite • 1920 Eddington shows Newton’s Universeis Unstable and would collapse • 1929 Inconsistent with Hubble’s Law (expanding universe)

8. 8 A.2a Olber’s Paradox (1823?) Heinrich Olber 1758-1840 discoverer of the minor planets Pallas and Vesta If the universe is infinite in extent, and filled with stars, Why is the sky dark at night? For example, in this cactus forest, if youlook between two cacti, you just seeanother cactus further away. In someplaces you see blue sky because theforest is not infinite, but if it was, you’djust see cacti everywhere, and so theuniverse would be “green”.

9. 9 A.2b Olber’s Paradox It’s the same with stars. If you look between two stars, you will just see another. Everywhere the sky should be as bright as the sun!

10. 10 A.2c Olber’s Paradox It’s the same with stars. If you look between two stars, you will just see another. Aren’t more distant stars fainter due to the inverse square law? Yes, but, at a greater distance, the number of stars per angle will increase by the distance squared! The two effects cancel out! Everywhere the sky should be as bright as the sun!

11. A.3a The Finite Universe Solutions to Olber’s Paradox might be that the Universe might be finite in: size (no galaxies far away) or time (no galaxies in distant past) 11

12. 12 A.3b Curved Finite Universe 1917 Einstein proposes universe: • Is finite, curved like a ball(this fixes Olber’s Paradox) • But gravity would still collapse it • Proposes negative pressure(cosmological constant) prevents collapse • Later calls this his “biggest blunder”

13. 13 A.3c Curved Space If we live in a (positively) curved space, then no matter what direction we look, we might see that back of our head! Its like living on the surface of a big ball. This would explain why sky is dark at night.

14. 14 A.3d Lookback Time Speed of light is a constant: c=186,282 miles/second The further away we look, the further into the past we are seeing! If the universe is unchanging, then there will be just as many galaxies far away (in the past) as nearby (in the present) [if we correct for the curve of space] But, if the universe had a beginning, then when we look far away, galaxies had not yet formed!

15. 15 A.3e Hubble Deep Field Survey • 10 days in December 1995 • Focus on one small “average” part of the sky and count all the galaxies out to the edge of the universe. • Area is about 0.04 square degrees (the size of a dime viewed at 75 feet, or one-27th-millionth of the complete sky

16. 16 A.3f Hubble Deep Field Survey • Found at least 3000 galaxies • Hence there must be about 3000 x 27,000,000=80 billion galaxies in the universe.

17. 17 A.3g Hubble Ultra Deep Field • in March 2004 -- the Hubble Ultra Deep Field survey probed even more deeply an area about three minutes of arc square, shows 10,000 galaxies. • The nearest galaxies - the larger, brighter, well-defined spirals and ellipticals - thrived about 1 billion years ago. • The smallest, reddest 100 galaxies, the most distant, existed when the universe was just 800 million years old. These are possibly the first galaxies to emerge from the so-called "dark ages," the time shortly after the big bang when the first stars reheated the cold, dark universe.

18. 18 A.3h Mass of Universe • A Galaxy is approximately 100 billion stars • Mass of Typical Star is: 2x1030 kg • Total Mass of Universe: 1.6x1052 kg • Neutrinos and photons might contribute some energy (equivalent to mass), but estimates are that its not significant (less than 0.1% of stellar mass) • We are ignoring “dark matter” here

19. B. The Expanding Universe Evidence suggests the universe is NOT static. It is expanding with time Hubble’s Law Lifetime of Universe Size and density 19

20. 20 B.1a Galactic Recession • 1912 Vesto Melvin Slipher first measures “doppler redshifts” of galaxies • 1917 Willem de Sitter interpreted Slipher’s red shifts as a Doppler effect, meaning that the galaxies are moving away from us (known for a time as the “de-Sitter effect). [He perhaps is the first to propose that the universe is expanding] • 1923 Carl Wirtz combined Slipher’s red shift measurements with rough estimates of the distances to galaxies based on their apparent size, and proposed a velocity-distance law, i.e. that redshift is proportional to distance. [This result has been historically ignored, and Hubble got most of the credit]

21. 21 B.1b Big Bang Theory • 1922 Friedmann, and 1927 Father Lemaitre show that another solution to Einstein’s equation would be that the universe is expanding from kinetic energy leftover from a “big bang” creation. No need for negative pressure. • This would also explain the observed “redshifts”

22. 22 B.1c Steady State Model • 1948 Sir Fred Hoyle (and others) propose that the universe may appear to be expanding, but its actually not changing. Matter is constantly created to keep the “flow” going. • “Every cluster of galaxies, every star, every atom had a beginning, but the universe itself did not." • He ridiculed LeMaitre’s theory by calling it the “big bang” theory. • 1960 Discovery of cosmic radiation (left over from big bang) torpedoed Hoyle.

23. 23 B.1d Hubble’s Law To visualize the expansion of our three-dimensional universe, imagine a two-dimensional universe crisscrossed by a grid of parallel lines (like on a piece of graph paper). The animation shows five galaxies that happen to lie where gridlines cross. As the universe expands in all directions, the gridlines and the attached galaxies spread apart. From the viewpoint of any one of the galaxies, all the other galaxies appear to be moving away. The more distant a galaxy is, the more rapidly it appears to be receding. • 1929 Hubble’s Law

24. The velocity is measured using the Doppler redshift (Z) Redshift Defined: Z = Dl/l Example: if wavelength is 520 nm, but you measure it to be 572 nm, then Dl=52 nm, and Z=52/520=0.1 Doppler Formula relates velocity to redshift v/c = Z (approximately, valid for v<<c) c=speed of light Example: Z=0.1 means the speed is 10% the speed of light. 24 B.1e Hubble’s Law (1929) (recessional speed) =(const)x(Distance) Or: v = H d H=Hubble’s Constant, which will be the “slope” of the line. The approximate value is 75 km/(sec-MPC) MPC=megaparsec (a million parsecs).

25. 25 B.1f Relativistic Doppler Formula If we have: Z=v/c, then what about distant quasars that have Z=3. Does this mean its traveling 3 times the speed of light? NO! As you approach the speed of light, the redshift goes to infinity. Redshift of Z=3 is speed of 88.25% speed of light. The true “relativistic” doppler formulae:

26. 26 B.2a Lookback Time [advanced] • Another way of looking at cosmological redshift is that the wavelengths have been stretched with the expansion of the universe. The ratio of received to emitted wavelength equals the change in size of the universe. • The lookback time is not just “today’s distance D” divided by c, because when the photon was emitted the galaxy was closer to us, but expanded while the photon was in flight. • For constant expanding universe, lookback time for galaxy at distance “D” today is given by,

27. 27 B.2b Hubble Time: 13 billion years If the universe has been expanding at a constant rate, then by “playing the movie backwards”, 13 billion years ago the universe was a single point (big bang!)

28. 28 B.3a Size of universe • If photons started at the big bang, then how far have they travelled during the lifetime* of the universe? • R = c/H0 = 4225 MPC(3x105 km/sec)/(71 km/s-MPC) = 4225 MPC • R=1.3x1026 meters *Note age of universe is the “Hubble Time” = 1/H0

29. 29 B.3b density of universe • From our data, the average density of the universe is about 1 proton per cubic meter! • Other evidence however suggests the number is more than 5 bigger due to “dark matter”

30. 30 B.3c Is the Universe a Black Hole? • Is our universe a big black hole in a larger universe? • Calculation says we’d need 5x more matter for it to be a black hole. • If include “dark matter” then YES!

31. 31 C. Eschatology The fate of the universe 1. Decelerating Universe • Open vs Closed Universe • Accelerating Universe

32. 32 C.1 Decelerating Universe We expect the universe is decelerating due to all the gravitational attraction between galaxies. Hence the age of the universe is somewhat less than the Hubble Time (13 billion years)

33. 33 C.2 Open vs Closed Universe CLOSED UNIVERSE: Just like a ball thrown upward will fall back to earth due to gravity, we might expect the universe will slow down, and collapse. OPEN UNIVERSE: If you throw a ball upward fast enough, it won’t fall back, but it certainly will slow down due to gravity We expect that the universe must be decelerating due to gravity. Whether the universe is open or closed is only a question of how fast it is slowing down.

34. 34 C.2b Critical Density [advanced] • Imagine test particle on “edge” of expanding universe with total energy ZERO.

35. 67 C.2c Density Parameter If the measured density  is greater than this “critical density” cthen the Universe in closed. Density Parameter:  = /c •  >1 Closed (+ Curved) •  =1 Flat (0 Curved) •  <1 Open (- Curved) Measured Density gives =0.27, a factor of 5 short of making the universe closed.

36. 36 C.2d Closed Universe [advanced] • If total energy is negative, the universe expands and contracts like a cycloid

37. 37 C.2e Deceleration Parameter “q” [advanced] • Hubble’s constant will change with time due to deceleration of the universe • For critical universe then q=½

38. 38 C.2f Measuring Deceleration Redshift is proportional to expansion rate Brightness of cluster is a measure of distance, which is a measure of lookback time into the past. Expect to see deviations from Hubble’s law in the past, when universe was expanding faster.

39. 39 C.3a The Universe is Accelerating? 1998 Measurements of distant supernova (i.e. in the distant past) were 20% fainter than expected. Interpretation: universe WAS slowing down for first half of lifetime BUT, since then, it has been ACCELERATINGq=-1 This is a big surprise

40. 3 C.3b Distant Supernova Data

41. 4 C.3c Dark Energy How do we explain this? • Propose Universe is • 4% normal stuff • 23% weird dark matter • 73% “DARK ENERGY” The Dark Energy provides the negative pressure. But is the universe really 96% weird stuff? • Alternative: Revive Einstein’s Cosmological Constant?

42. 5 C.3d Possible Models

43. 43 V. Summary The “Copernican Cosmological Principle” is that • (a) The sun is the center of the universe • (b) There is no center to the universe • (c) The universe is a ball of curved space • (d) The earth is the center of the universe • (e) none of these

44. 44 Question 2 The evidence favors that the Universe: • (a) is homogeneous in time • (b) is constantly creating matter • (c) had a “big bang” beginning • (d) is infinite in size • (e) none of these

45. 45 Question 3 If Hubble’s constant is 75 km/s-MPC, a galaxy 3 MPC away will be receding at: • (a) 25 km/s • (b) 75 km/s • (c) 78 km/s • (d) 225 km/s • (e) none of these

46. 46 Question 4 What is the best argument against the Steady State model of the universe? • (a) Detection of primordial radiation • (b) Detection of Galactic redshifts • (c) Hubble’s law • (d) Olber’s Paradox • (e) none of these

47. 47 Notes • http://www.phys.unsw.edu.au/astro/cosmo/jkw_lecture/sld034.htm