Lecture 29: Cosmology
Astronomy 101/103
Terry Herter, Cornell University
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Lecture
Topics
  • The expanding universe
  • Cosmology
    • The cosmological principle
  • The Age of the Universe
  • The Big Bang
  • Look-back times


The Expanding
Universe
  • Hubble compared the distances he measured for galaxies with their Doppler shift of spectral lines.
  • He discovered that the universe is expanding!
    • Galaxies show redshifted spectral lines.
  • The greater the distance, the higher the recession velocity.

Hubble's Law
  • Recession velocity is proportional to distance:

Distance and
Redshift
  • Using Hubble's law, the distance to a galaxy can be determined by its redshift, z.

  • At low velocities, z ~ v/c (the Doppler effect).
  • Redshift resulting from the Hubble flow is often called the cosmological redshift.

Cosmology
  • Cosmology is the study of the structure and evolution of the universe.
  • On every scale observed so far the universe shows structure:
    • stars form star clusters and galaxies
    • galaxies form galaxy clusters and superclusters, and other large structures

Large-scale
Structures
  • Structures ~ 200 Mpc in size have been seen.
  • This is much less than the most remote QSOs which are ~ 4000 Mpc distant.
  • The most extensive surveys cover only ~ 1/1000 of the observable universe!
    • Similar to trying to determine the appearance of the earth from a map of Rhode Island.
  • A 300 Mpc cube anywhere in the universe contains ~100,000 galaxies.
    • excluding faint dwarf ellipticals and irregulars
  • The total number of galaxies is roughly
    (4p/3)(4000/300)3 ~ 109 galaxies
  • More recent and better estimates give 125-150 billion galaxies.
Note: The argument above (using the light travel time to calculate the distance) is not really correct since the geometry of the Universe is not Euclidean. In addition, galaxies in the past were different because they were just being formed. Many present day galaxies are made up of a number of originally smaller galaxies which merged together.

The Cosmological
Principle

Cosmologists make two assumptions known as the cosmological principle:

  1. The universe is homogeneous.
    • smooth on the largest scales
  1. The universe is isotropic.
    • looks the same in every direction

Note: These assumptions are based on sketchy data, theoretical insight, and philosophical preference.


No Center to
The Universe

  • Hubble's law is very special.
  • If we are galaxy A, the velocities are:

  • What do people on galaxy B see?

  • The same expanding universe!


Olbers's Paradox

  • For a static, uniform density, infinite universe the sky should be bright!
    • Everywhere you look you should see a star.
  • Answer:
    • The universe is not infinite due to its finite age.
    • It is not unchanging in time.

The Age of the
Universe
  • Hubble's law tells us that for galaxies:
  • v = Ho x d

  • Since the universe is expanding, galaxies were closer together in the past.
  • Extrapolating backwards, all the galaxies were on top of one another!
  • When was this?


How it Looks



The Age of the
Universe
(cont'd)
  • If the universe has been expanding uniformly, the time for this is:
  • Inserting Hubble law:
  • Suppose Ho = 100 km/sec/Mpc, an estimate of the age of the universe is:


The Big Bang

The present location and velocities of galaxies are a result of a primordial blast known as the BIG BANG. It marked:

  • THE BEGINNING OF THE UNIVERSE!
  • THE BEGINNING OF TIME!

What is the
BIG BANG?
  • The Big Bang was NOT an explosion in an otherwise empty universe.
  • The Big Bang involved the entire universe.
  • At the beginning the Big Bang happened everywhere at once.


Look Back
Times
  • As we look further out in the universe we are seeing it at earlier times!
    • It takes a long time for light to get here.
  • Telescopes are thus "time machines" which allow us to look at the early universe.


Look Back Times

Look Back Times

z

v/c

Look-back time
(109 years)

"Distance"
(Mpc)

Luminosity Distance (Mpc)

0.1

0.095

1.29

394

455

0.25

0.22

2.92

895

1249

0.5

0.385

5.02

1540

2823

1.0

0.60

7.73

2373

6635

2.0

0.80

10.3

3167

15740

5.0

0.946

12.5

3826

47610

inf.

1.0

13.67

4194

infinity

We assume here that Ho = 71 km/sec, WM = 0.27, and WL = 0.73.
Note: The "Distance" above is just the Look-back time multiplied by the speed of light. This is not really the distance astronomers quote for an object in the distant universe. Astronomers use the "Luminosity Distance" to tell how bright an object appears (the inverse square law). This is listed in the last column. There are two reason why these values are different, the galaxy is moving away from us (which causes photons to be redshifted and a time dilation effect) and the geometry of the Universe is not necessarily Euclidean.
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