Key Concepts:

1. Why is the night sky dark (Olbers' paradox)?
2. What does it say about the nature of the Universe?
3. What is the Big Bang and what evidence do we have?
4. What is Hubble Expansion?
5. What is the age of the Universe?
6. What does the expansion of the Universe mean, exactly?
7. What is the cosmic horizon?

Exam 3 and Final Exam

Rare Earth paper due today

Cosmological Principle: The universe is homogeneous and isotropic when average over large scales, and no special location exists.

Quiz 23A: an exercise in probability and logic

History

1. According to Aristotle (350 BC), the Universe is eternal and has never changed. The Earth is at the center, and the stars are located at the outer boundary, where all things including the space itself fade into nothingness.
2. Several astronomers and philosophers such as Kepler (1610) and Halley (1720) have pointed out that the dark night sky implies the finite extent of the Universe.
3. Heinrich Olbers (1823) presented the full argument and offered an (incorrect) explanation ("dust blocks the light").

Assumptions:

1. Universe is infinite in extent.
2. Stars (and galaxies) are uniformly distributed in all directions.
3. Universe was and always will be around.

Consequence: Every line of sight would cross the surface of a star, and the night sky should be as bright as the star's surface in all directions!

• Consider a series of concentric shells of stars surrounding you. Mathematically:
• brightness of a star at a distance D₁: f₁ = L/[4πD₁²]
• total energy arriving from the the shell at D₁: dL₁ = n x f₁ (n is number of stars)
• brightness of individual star in each shell becomes fainter following the inverse square law: f = f₁/[D/D₁]²
• the number of stars in each subsequent shells goes up as distance squared: N = n x [D/D₁]²
• the net amount of light contributed by each shell remains constant, independent of the shell distance: dL = N x f = (n x [D/D₁]²₁) x (f₁/[D/D₁]²) = n x f₁ = dL₁
• when added all up, the total amount of light arriving at your location from all of the shells out to infinity is infinitely large: E = N_shell x dL

(Possible) Resolution of the Paradox

1. Dust absorbs light and obscures what lies beyond.
2. There are only finite number of stars in the Universe.
3. Stars are not uniformly distributed.
4. The Universe is expanding, so distant stars are redshifted to become invisible.
5. The Universe is young, and not all light has reached us.

Further Questions:

1. What about dust?
2. What about dark matter?
3. Why is the sky bright during the day?

Hubble Law

In 1920, Edwin Hubble discovered that more distant galaxies have larger recession velocities, following the relation

The constant H that relates the recession speed V and distance D is refereed to as the Hubble constant.

Cosmological Principle: The universe is homogeneous and isotropic when average over large scales, and no special location exists.

Age of the Universe ("Hubble Time")

Turning this around, one can infer the distance of a galaxy with measured recession speed V as D = V/H. For the recession velocity in km/s, H = 65 gives D in megaparsecs (Mpc; million parsecs).

A crude age estimate of the universe can be derived as t = D/V = 1/H. Such a calculation suggests the age of universe between 12 and 15 billion years.

Quiz 23b

Meaning of Redshift

Review: Doppler shift

Redshift is a measure of the expansion of space, rather than that of a speed

Quiz 23c

Cosmic Horizon

• speed of light is finite
• age of the universe is also finite
• cosmic horizon: the maximum distance that light can travel in the universe's age
• the size of cosmic horizon increases with time
• what lies beyond?
• what if the Hubble constant was 10 times larger or smaller?

Quiz 23E

Three Main Observational Evidence for the Big Bang

Web Resources on Cosmology

• NASA Microwave Anisotrophy Probe (MAP) Project Cosmology Tutorials
• Cambridge University Cosmology Page
• Cosmology Tutorials by N. Wright
• "Cosmos in a Computer" by NCSA/UIUC

Reading assignment for next lecture: Unit 80-81