Expansion of
the Universe

Until well into this century, it was not understood whether the great groupings of stars that were seen through telescopes were part of our own galaxy, or distant galaxies in their own right. This puzzle was finally resolved by using Cepheid variables to establish a distance to the objects like the "spiral nebula" in the constellation Andromeda, and to determine the size of our own galaxy. By around 1925, Hubble, Leavitt, Hertsprung, Shapley, and others had established conclusively that objects like the Andromeda "Nebula" were in fact much further away than objects in our own galaxy and thus were themselves galaxies.

The Expansion of the Universe

Then, in the late 1920's, Hubble, building on results obtained earlier by Slipher, combined Doppler shift measurements of radial velocities with distance measurements to conclude that almost all galaxies were flying away from the Milky Way, and that the velocity of recession was proportional to the distance from us: the further the galaxy from us, the faster it was receding.

It later turned out that there were systematic errors in the earliest measurements, associated primarily with a failure to realize that there were two kinds of Cepheids, failure to disguish in some cases Cepheid and RR-Lyra variables, and failure to account for the scattering of starlight by interstellar dust. However, although corrections for these mistakes changed the distance scales by as much as factors of two, they did not alter the fundamental conclusions:

  1. There are many galaxies outside of our own.
  2. These galaxies are all receding from us if we go to large enough distances.
  3. The velocity of recession is proportional to the distance from us.

Olber's Paradox

That the Universe is not static but expanding helps solve a paradox that has been known at least since the 1500s but that was popularized by Heinrich Olbers in 1826 and has come to be known as Olber's Paradox. Briefly, if the Universe is static and uniformly filled with stars and galaxies, one can show that the night sky should be as bright as the surface of a star. That this is not so constitutes the paradox. The expansion of the Universe solves this problem, as is discussed nicely in this reference.

The Distant Galaxies are Flying Away from Us

The galaxies are all flying apart (on very large distance scales), with the velocity of recession proportional to the distance between them. The adjacent image, taken by the Wide-Field and Planetary Camera (WFPC2) of the Hubble Space Telescope, shows many galaxies billions of light years away. Most of the fuzzy patches are galaxies containing billions of stars; click on the image to get a larger version. The galaxies in this image are receding from us at high velocities.

The details of this expansion are dictated by the value of the Hubble Constant. The objects furthest away from us appear to be receding at near the velocity of light. This expansion of the universe is a result of the original explosion that created the universe-the big bang. The big bang did not happen in space and in time; our modern understanding is that space and time as we presently experience them are themselves created in the big bang. Therefore, it makes no more sense to ask what was before the big bang than to ask what is north of the north pole.

Here is a Java applet (written by someone else) that can be used to illustrate the Hubble Law. However, the reader is warned that it is very slow loading and may not run properly if you do not have the latest browser.

A Two Dimensional Analogy

The Universe has 3 spatial dimensions, but it is easier to visualize an analogy to its expansion for the 2-dimensional surface of a balloon. There is no center. If you stand on any galaxy, all the others will appear to be moving away from you with a velocity proportional to the distance from you. An analogy in 2 dimensions is to put dots on the surface of a balloon and blow the balloon up. As it expands, there is no dot that is the "center", but if you stand on any dot you will see all other dots moving away from you (and the rate at which they move away will be proportional to the distance. Dots close to you will be moving away slower than those further away). The expansion of the Universe appears to be like this, but in 3 rather than 2 space dimensions, which makes it much harder to visualize, but it is possible to describe it mathematically.

Comoving Coordinates

It is often simpler to discuss things happening in the expansion of the Universe if we adopt a vantage point that is moving uniformly with the expansion. Astronomers call such a vantage point a comoving coordinate system. The balloon analogy in 2 dimensions illustrates simply the idea of comoving coordinates. If instead of viewing the expansion of the balloon from the outside I place myself on one of the dots on the balloon's surface, I appear to be stationary and I see the other dots moving away from me (and in my immediate area I see the apparent curvature of the balloon's surface decreasing). Astronomers will also often speak (in 3 dimensional space) of a comoving volume. This means a volume of space that is moving uniformly with the expansion.

Illustration of Comoving Coordinates in 2 Dimensions

Here are two MPEG movies illustrating the formation of structure in the Universe that illustrate the difference between viewing the surface of a balloon from outside or from comoving coordinates on its surface: Here are some still frames from the corresponding movies:

View from
View from

Comoving coordinates in the real Universe correspond to extending this idea to 3 spatial dimensions.

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