University of California, San Diego
Physics 7 - Introduction to Astronomy

H. E. Smith   Winter 2007

Physics 7 - Lecture Summary #19

Cosmology: The Structure & Future of the Universe

First, there are probably some questions on your mind:

  1. If the Universe is expanding, what is it expanding into?
    • Ask Dr. Science.
    • Nothing, the very fabric of space and time are expanding.
    • For a more complete & satisfactory answer ask Dr. Ned Wright at UCLA.

  2. What happened before the Big Bang?
    • We don't know. Quite probably we can't know. Before about 10-43s our current laws of physics are inadequate to describe the Universe. For example, we would need a theory of Gravity that is consistent with Quantum Mechanics, which we don't yet have. Even as our understanding of Physics improves, we may get closer and closer in time to the Big Bang, but may be prohibited from understanding the "moment of creation" or what came before.
    • Dr. Bruce Margon & Dr. Craig Hogan at the Univ. of Washington have a good answer.
    • Dr. Ned Wright has an answer for this one too.

  3. If everything is moving away from us, doesn't that put us at the center of the Universe?
    • No, everything is moving away from everything else; everyplace looks like the center, but there really is no center.
    • Ned Wright's Balloon Analogy helps.

The Geometry of the Universe

General Relativity allows for three geometries of Spacetime in the Universe depending on the density of the Universe and the Universal fate:
Hyperbolic (Open) Geometry
  • Parallel lines diverge.
  • Vsphere > 4/3 R3.
  • Universe is unbound (expands forever).
  • < 1 ( < 10-29g/cm3).

Flat (Euclidean) Geometry

  • Parallel lines remain at a constant distance.
  • Vsphere = 4/3 R3
  • Universe continuously slows down.
  • = 1 ( = 10-29g/cm3).

Spherical (Closed) Geometry

  • Parallel lines converge.
  • Vsphere < 4/3 R3
  • Universe is bound (will collapse back)
  • > 1 ( > 10-29g/cm3).

Diagram from Ned Wright's Cosmology Tutorial © Edward L. Wright (UCLA), used with permission.


Scale of the Universe vs Time

We Live in a Curved Space

Before you go off thinking that this is all to wierd to try to grasp, remember that we live on a spherically curved surface, called Earth. Lines of longitude, parallel at the equator, follow the surface of the Earth, converging at the poles.

Also, circles may not be what they seemed in high school geometry. Suppose you started drawing circles around the North Pole, keeping the pole at the center. Measuring the relation between Circumference and radius, you would find that for small circles:

C = 2R

(Space always seems flat on small scales; that's why there are still people who believe the Earth is flat!). But continuing to draw ever increasing circles (lines of latitude) you will finally draw the biggest circle that you can on the earth - around the equator. Now the circumference of the circle is the circumference of the Earth. The radius, measured along the curved surface from the pole to the equator is 1/4 of the circumference of the earth:

C = 4R < 2R



Diagram from Ned Wright's Cosmology Tutorial
© Edward L. Wright (UCLA), used with permission.

Cosmological Tests

  1. Measure the density of matter directly. Well we can't do that; the best we can do is to measure the density of luminous matter in the Universe - count the number of galaxies in a region of space, then multiply by the mass of a galaxy. When we do this, we find that the density of luminous matter in the Universe is about 1% of the critical density (lum ~ 0.01 or ~ 10-31g/cm3). But what mass do we use for a galaxy? That is what about Dark Matter? If we correct for the amount of known dark matter, say by the factor of 10 required to bind galaxy clusters we are at about 10% of the critical density. But we really don't know how much dark matter is out there. It is entirely plausible that

  2. Big Bang Nucleosynthesis

  3. Scientific American: Primordial Deuterium by Craig Hogan.

  4. The Hubble Diagram



    Ned Wright's (UCLA) Analysis of the Hubble Diagram for SNIa
    Red Line is Closed Universe ( = 2)
    Black Line is Flat Universe ( = 1)
    Green Line is Open Universe ( = 0)
    © Edward L. Wright (UCLA), used with permission.

    Cosmology Links

    Big Bang   Physics 7 Lectures   Physics 7 Home  

    Conducted by Gene Smith, Physics/CASS, UCSD.
    Comments? You may send email to hsmith@ucsd.edu

    Prof. H. E. (Gene) Smith
    CASS   0424   UCSD
    9500 Gilman Drive
    La Jolla, CA    92093-0424


    Last updated: 28 Jan 2000