Foundations of Modern Cosmology

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Chapter 10: The Expanding Universe

Chapter Summary

This chapter recounts several important historical threads in the development of modern cosmology. Controversy over the nature of "spiral nebulae" had persisted since the late 18th century, with one camp insisting they were external "universes," while their opponents were equally convinced that the spiral nebulae were localized clusters of stars within our Galaxy. An important early discovery was Shapley's determination of the size of the Milky Way Galaxy, and of our location within it. Shapley found the Milky Way to be much larger than previously believed, and on this basis he erroneously concluded that the spiral nebulae must be relatively nearby clusters. Shapley and Curtis participated in a famous debate in 1920 over the nature of the spiral nebulae, but insufficient data prevented a resolution of the puzzle. Finally, Hubble determined that the Andromeda Nebula (now known as the Andromeda Galaxy) was much too far to lie within the confines of the Milky Way; Hubble had discovered external galaxies. In the first quarter of the twentieth century, humanity's view of the cosmos leaped from a fairly limited realm of the Sun surrounded by an amorphous grouping of stars, to one in which the Milky Way is just a typical spiral galaxy in a vast universe filled with galaxies.

Not long after Hubble's discovery of external galaxies came his discovery of a linear relationship between their redshifts and their distances, a relationship known today as the Hubble Law. Determining the value of the constant of proportionality, the Hubble constant, remains an important research goal of modern astronomy. The Hubble "constant" is not really constant, because it can change with time, though at any given instant of cosmic time in a homogeneous, isotropic universe, it is the same at all spatial locations. The inverse of the Hubble constant, called the Hubble time, gives an estimate of the age of the universe.

The development of the theory of general relativity provided the framework in which Hubble's discovery could be understood. Einstein found that his equations would not admit a static, stable model of the universe, even with the addition of the "cosmological constant.". The timely discovery of the redshift-distance relationship provided evidence that the universe was not static, but was expanding. The Robertson-Walker metric is the most general metric for an isotropic, homogeneous universe that is also dynamic; i.e. it changes with time. An important parameter in this metric is the scale factor, the quantity which describes how lengths in the universe change with cosmic time. The scale factor can be used to derive the cosmological redshift, the change in wavelength of light as it traverses the universe.

Measuring Hubble's constant requires accurate distances to increasingly remote galaxies. One of the best distance measures is the Cepheid variable star. The HST has now been able to detect Cepheid variable stars in the galaxy M100 in the Virgo galaxy cluster. Several Cepheids have been found such as this one. These new data give us a distance to M100 of 17 Mpc and is consistent with a rather large Hubble constant of about 80 km/sec/Mpc.

There are several important concepts and ideas in this Chapter.

  • The definition of redshift.
  • The distance ladder
  • The Hubble law
  • Einstein's cosmological constant
  • Robertson-Walker metric and the scale factor
  • Hubble constant, Hubble time, Hubble sphere
  • Cosmic redshift

Hubble Edwin Hubble

Points to Ponder

How does cosmological redshift relate to the scale factor? What do graphs of scale factor R versus t mean? How is the Hubble constant term H related to the scale factor? What does "expanding space" mean?

What does a Hubble flow do to the spatial distribution of galaxies? Consider the following image. On the left we have a bunch of galaxies, uniformly distributed. In the center we pick out a galaxy and show the Hubble flow. After some amount of time, expansion leaves the galaxies distributed as on the right.

Location in the expanding universe does not matter. Expansion is uniform and looks the same everywhere. Each galaxy sees the other galaxies moving away in accordance with the Hubble law. Another example is provided by these figures showing the expansion of a 2D sphere.

Potential Pitfalls The major difficulty is reconciling the observation that the universe is expanding, and that it is expanding away from us according to the Hubble law, but we are not at the "center" of the universe. Indeed, there is no center. People sometimes ask, if there is an expansion doesn't there have to be a center of the expansion? No. Space is expanding (or stretching out, if you will) everywhere, not expanding away from some point.
Questions & Answers

Questions and Answers related to Chapter 10.

Web World

An additional internet source on galaxies can be found at the Galaxy Primer page.

Here is a paper about the history of the Curtis-Shapley Debate which took place in 1920. This paper was written in conjunction with a National Academy anniversary debate on the nature of the gamma ray burst sources.

On-line biographies of: Edwin Hubble

For more information, try working through the lab Determining the Extragalactic Distance Scale available from Northwestern University.