Hubble's Law and the Expansion of the Universe

The Hubble law states that the more distant objects recede from the Milky Way galaxy at larger speeds than more nearby objects. The precise relationship is V = H(now) x D, where H(now) is known as the Hubble constant and is a measure of how long it takes the Universe to roughly double in size (actually to e-fold in size). The currently accepted value for the Hubble constant is ~ 25 - 30 km per second / one million light years, although there is controversy surrounding this number (more on this later on). An interesting result can be deduced from the Hubble constant without referring to a specific model for the Universe (other than it is expanding).

Age of the Universe

• If we imagine that the Universe has been expanding at a constant rate, we can deduce roughly how long ago the objects in the Universe were sitting on top of each other (and thus the age of the Universe). If an object at distance D is moving away from us at speed V, then it is easy to figure out how long the object has been running away from us. We have

• speed = distance / time ===> time = Age of Universe ~ D / V = 1 / H(now) !

• Using the value for the Hubble constant given above, we arrive at an age of ~ 12 billion years!! Note that if the Universe has only decelerated since its birth, this number is an upper limit to the age of the Universe.

  The current best estimate for the age of the Universe is 13.7 billion years

  This has the potential of being annoying since there are stars which may be older than this. The ancient star clusters known as globular clusters:

  Globular clusters are ancient star clusters composed of tens of thousands of stars to millions of stars. They are found in the halo of our Galaxy and represent among the oldest of the known stars in our Galaxy. Using stellar evolutionary arguments (see the Hertzsprung-Russell diagram to the right (and Astronomy 122), we can infer the ages of the stars in a globular cluster.

  globular clusters can be as old as 14 - 16 billion years (based on our understanding of stellar evolution). The oldest white dwarf stars in our Galaxy are 12-13.4 billion years old.

---

Interpretation of the Hubble Law

Explosion A natural explanation is that an explosion occurred and that we are at the center of the Universe. Consequently, the galaxies are flying away from us in all directions and that the ones with larger initial kicks are now farther off.

Uniform Expansion The current preferred explanation is that the Universe expands uniformly (with no center). In this scenario, any observer in the Universe sees essentially the same thing and all observers find the same Hubble's Law!

Initially, the choice was not obvious as to which of the above was correct. However, by this time people were loathe to believe that we occupied a preferred spot in the Universe. The Hubble law was interpreted as an indication of the uniform expansion of the Universe.

Return to Copernican Principle