1. Please pick up your corrected problem set and midterm. Problem Set #4: median score = 85 Midterm Exam: median score = 72

2. Recap: The Story So Far… Monday, November 3 Next planetarium show: Thu, Nov 6, 6 pm.

3. History of cosmology: Version 1.0: “Superdome” model

4. Version 2.0: Geocentric model spherical Earth at center

5. Version 3.0: Heliocentric model Sun at center

6. Infinite v. 3.1: Infinite heliocentric model

7. v. 4.0: Big Bang model

8. space-time curvature v. 4.1: Big Bang model with space-time curvature. observed Mass & energy cause space to curve. This curvature causes an observed bending of the path of light.

9. Curvature on large scales: Positive curvature Positive curvature: gravitational lensing makes distant objects loom large. Negative curvature Negative curvature: gravitational lensing makes distant objects appear tiny.

10. Measured curvature on large scales: flat Observed angular sizes of distant galaxies: consistent with flat space. bigger than the observable universe If space is curved, its radius of curvature is bigger than the observable universe.

11. Expansion on large scales:

12. As light travels through space, its wavelength expands along with the expansion of space.

13. highest known redshift Galaxy with the highest known redshift: IOK-1 z = 7 Name: IOK-1 Redshift: z = 7

14. Redshift z=7. What does this mean? Hydrogen has an emission line at λ 0 = 122 nm. In this galaxy, the line is seen at λ = 8 × 122 nm = 976 nm. 1 nm = 1 nanometer = 10 -9 meters

15. Redshift z=7. What does this mean? 122 nm 8 × 122 nm Light emitted with wavelength λ 0 = 122 nm has been stretched to λ = 8 × 122 nm = 976 nm. a = 1/8 a = 1 Universe has expanded from a scale factor a = 1/8 (when light was emitted) to a = 1 (when light is observed).

16. If we observe a distant galaxy with redshift z, the scale factor a at the time the galaxy’s light was emitted was: Example: z = 1 implies a=1/(1+1) = ½. Lengths (including wavelengths of light) have doubled since light was emitted.

17. Photons from distant galaxies aren’t stamped with “born on” dates. However, they are stamped with the amount by which the universe has expanded since they were “born”. (measurable) redshift scale factor

18. When was the light we observe from this galaxy emitted? A convenient aspect of a “Big Bang” universe: the start of expansion gives an “absolute zero” for time.

19. Different calendars have a different “zero point” (birth of Christ, hijra to Medina, etc.) time For a cosmic time scale, there’s also a logical “absolute zero”: the instant at which expansion began. temperature For a temperature scale, there’s a logical absolute zero: the temperature at which random motions stop.

20. t = 0 (start of expansion, alias “The Big Bang”) t ≈ 14 billion years (now) t ≈ ??? (first galaxies)

21. When was the light we observe from this galaxy emitted? t ≈ 750 million years (when the universe was only 5% of its present age).

22. How far away is this galaxy? The galaxy’s light took about 13 billion years to reach us. If the universe weren’t expanding, we could say “it’s about 13 billion light-years away”. IS But the universe IS expanding!!!

23. How far away is this galaxy? Farther away than it used to be! t e = time light was emitted t o = time now d e = distance when light was emitted d o = distance now t e < t o d e < d o

24. When the light we observe now was emitted: d e = 1700 megaparsecs Now, when we observe the light: d o = 8 × d e = 8 ×1700 = 13,600 megaparsecs = 5.5 billion light-years = 44 billion light-years

25. Point to ponder: 5.5 billion light-years (initial distance) is less than 13 billion light-years (distance if static) is less than 44 billion light-years (current distance)

26. Point to ponder: = more than 3× Hubble distance! Current distance to z=7 galaxy = 44 billion light-years = 13,600 megaparsecs = more than 3× Hubble distance! As z → infinity, current distance → 3.2 × Hubble distance

27. The most distant object we can see (in theory) is one that emitted a photon at t=0. huge We will see this photon with a huge redshift z, since the universe has expanded hugely since the “Big Bang”. Photons emitted at t=0 come to us from the cosmological horizon.

28. The cosmological horizon is at a distance of 3.2 × the Hubble distance (about 14,000 megaparsecs, or 46 billion light-years). Longer than the Hubble distance because of universal expansion.

29. Wednesday’s Lecture: Reading: Chapter 8 Photons & Electrons Problem Set #5 handed out.