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Cosmology
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2. The Olbers Paradox Why is the sky dark at night?
Why is the sky dark at night?
If the Universe is infinite, every line of sight should end on the surface of a star.
The night sky should be as bright as the surface of stars!

3. Solution to the Olbers Paradox:
If the Universe had a beginning, then we can only see light from galaxies that has had time to travel to us since the beginning of the Universe.

4. Which other evidence to we have that the Universe had a beginning?
The finite ages of stars.
The finite ages of galaxies.
Hubble’s Law.
The evolution galaxies.
All of the above. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. Hubble’s Law
Distant galaxies are receding from us with a speed proportional to distance

6. The Expanding Universe
On large scales, galaxies are moving apart, with velocity proportional to distance.
It’s not galaxies moving through space.
Space is expanding, carrying the galaxies along!
The galaxies themselves are not expanding!

7. If all galaxies are receding from us, does that mean that we must be in the center of the Universe?
Yes.
No, you would have the same impression from any other galaxy as well.
No, we must rather be near the edge of the universe. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

8. The Expanding Universe
If recession speed is proportional to distance, every galaxy is receding from every other galaxy in the Universe.

9. Finite, but without Edge?
2-dimensional analogy: Surface of a sphere:
Surface is finite, but has no edge.
For a creature living on the sphere, having no sense of the third dimension, there’s no center (on the sphere!): All points are equal.
Alternative: Any point on the surface can be defined as the center of a coordinate system.
“Athens, OH: It’s not the end of the world. – But you can see it from here!”
“In an appropriately chosen coordinate system, Athens, OH, is the center of the Universe!”

10. The Cosmological Principle
1) Homogeneity: On the largest scales, the local Universe has the same physical properties throughout the Universe.
2) Isotropy: On the largest scales, the local Universe looks the same in any direction that one observes.
3) Universality: The laws of physics are the same everywhere in the Universe.

11. What is the logical connection between homogeneity and isotropy?
If the Universe is homogeneous, it must be isotropic.
If the Universe is isotropic, it must be homogeneous.
Both 1. and 2. (i.e., homogeneity and isotropy are equivalent)
None of the above. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

12. If the Universe is homogeneous, it must be isotropic.
If the Universe is homogeneous, it must be isotropic.
If the Universe is homogeneous, then it can’t make a difference which way you observe; you should always see the same structure.
However, it can be isotropic, but not homogeneous:

13. Shape and Geometry of the Universe
Back to our 2-dimensional analogy:
How can a 2-D creature investigate the geometry of the sphere?
Measure curvature of its space!
Closed surface
Flat surface
Open surface
(positive curvature)
(zero curvature)
(negative curvature)

14. According to the theory of General Relativity, gravity is caused by …
The equivalence principle.
The increasing mass of a relativistically moving object.
The curvature of space-time.
The mass-energy equivalence.
The constant speed of light.

15. Cosmology and General Relativity
According to the theory of general relativity, gravity is caused by
the curvature of space-time.
The effects of gravity on the largest cosmological scales should be related to the curvature of space-time!
The curvature of space-time, in turn, is determined by the distribution of mass and energy in the Universe.
Space-time tells matter how to move;
matter tells space-time how to curve.

16. The Big Bang This must have happened ~ 14 billion years ago
Tracing back the expansion of the Universe
There must have been a beginning with extremely high density and temperature: the Big Bang!
This must have happened ~ 14 billion years ago
The age of the Universe
Universe cools down as time passes
Universe expands as time passes

17. The Early History of the Universe
Electron
Positron
Gamma-ray photon
Electrons, positrons, and gamma-rays in equilibrium between pair production and annihilation

18. The Early History of the Universe
25 % of mass in Helium 75 % in Hydrogen
Protons and neutrons form a few helium nuclei; the rest of protons remains as hydrogen nuclei
Almost no elements heavier than Helium are produced.

19. The Early History of the Universe
Photons have a blackbody spectrum at the same temperature as matter.
Photons are incessantly scattered by free electrons; photons are in equilibrium with matter
Radiation dominated era

20. The Early History of the Universe
Protons and electrons recombine to form atoms => Universe becomes transparent for photons
z = 1000
Transition to matter dominated era

21. The Cosmic Microwave Background
After recombination, photons can travel freely through space.
Their wavelength is only stretched (red shifted) by cosmic expansion.
Today, this “cosmic background radiation” can still be observed!
Recombination: z = 1000; T = 3000 K

22. At a time corresponding to z = 1000, the background radiation had a blackbody temperature of 3000 K. At what wavelength does that spectrum peak?
:44
3 mm
1 mm
3 nm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

23. Wien’s Displacement Law:
Wien’s Displacement Law:
lmax = 3,000,000 nm / T[K]
= 1,000 nm = 1 mm
For T = 3000 K.

24. If this background radiation with lmax = 1 mm has been redshifted by z = 1000 until today, at which wavelength does it peak today?
:44
3 mm
1 mm
3 nm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

25. This corresponds to a blackbody of temperature T = 3 K.
The wavelength has been stretched by a factor of z = 1000:
lmax = 1 mm → 1 mm
This corresponds to a blackbody of temperature T = 3 K.
(More precisely, it’s actually K).

26. The Cosmic Microwave Background
If the Universe was perfectly homogeneous on all scales at the time of reionization (z = 1000), then the CMB should be perfectly isotropic over the sky.
Instead, it shows small-scale fluctuations:

27. The Cosmic Microwave Background
Angular size of the CMB fluctuations allows us to probe the geometry of space-time!
CMB fluctuations have a characteristic size of 1 degree.
Universe has a flat geometry

28. Knowing the basic principles of general relativity, the curvature of space-time reveals information about …
:30
the total content of mass (and energy) in the Universe.
the number of stars in the Universe.
the age of the Universe.
the abundance of heavy elements in the Universe.
the number of dimensions of the multi-dimensional space-time. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

29. The Future of the Universe
Will the expansion continue forever?
Or will it come to a halt and be reversed towards a “Big Crunch”

30. Assume you have a catapult that can shoot a ball up into the air so that it would just-so escape Earth’s gravity. Now, if you use that same catapult with the same ball on a planet that has twice the mass, but the same radius as our Earth. What will happen to the ball?
:42
The ball will also escape that planet’s gravity and actually have excess velocity at the end.
The ball will also just-so escape that planet’s gravity.
The ball will fall back onto the planet’s surface.
The ball will go into an orbit around the planet. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

31. Deceleration of the Universe
Deceleration of the Universe
Cosmic expansion should be slowed down by the mutual gravitational attraction of the galaxies.
Fate of the Universe depends on the matter density in the Universe.
Define “critical density”, rc, which is just-so enough to slow the cosmic acceleration to a halt at infinity.

32. The Future of the Universe
r < rc => Universe will expand forever
Maximum age of the Universe:
~ 1/H0
r = rc => Flat Universe
Size scale of the Universe
r > rc => Universe will collapse back
Time
If the density of matter equaled the critical density, then the curvature of space-time by the matter would be just-so sufficient to make the geometry of the Universe flat!

33. What causes a Type Ia Supernova?
The collapse of the iron core of a very massive star into a neutron star at the end of its life.
The collapse of the iron core of a very massive star into a black hole at the end of its life.
The collapse of a white dwarf that has accreted too much material in a binary system.
The explosive onset of hydrogen fusion on the surface of a white dwarf in a binary system.
The collapse of the Carbon/Oxygen core of a sun-like star into a white dwarf at the end of its life.
:42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

34. Measuring the “Deceleration” of the Universe …
By observing type Ia supernovae, astronomers can measure Hubble’s Law at large distances
Distance ↔ recession speed
Size scale of the universe ↔ rate of expansion
It was expected that this would measure the deceleration of the universe, but …

35. Measuring the Deceration (?) of the Universe
Decelerating Universe
Measured Brightness of Type Ia Supernovae
Distance → Look-back time
Hubble’s Law
Accelerating Universe
Redshift z (→ Expansion speed)

36. The Accelerating Universe
Flat decelerating Universe
Apparent Magnitude of Type Ia Supernovae
Flat accelerating Universe
Red Shift z
In fact, SN Ia measurements showed that the Universe is accelerating!

37. :43
If the Universe is currently accelerating and expanding at the measured rate, how should the cosmic size scale evolve with time? B) C) E) D) A) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

38. The Cosmological Constant
Cosmic acceleration can be explained with the “Cosmological Constant”, L
(“Lambda”)
L is a free parameter in Einstein’s fundamental equation of General Relativity; previously believed to be 0.
Energy corresponding to L can account for the missing mass/energy (E = m*c2) needed to produce a flat space-time.
Science Mag. 1998
→ “Dark Energy”

39. The Stuff the Universe is Made of
We only “see” about 4 % of all the mass and energy in the Universe!
The nature of about 96 % of our Universe is yet mysterious and unknown!