ASTRO 801
Planets, Stars, Galaxies, and the Universe

The Age of the Universe

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If we agree that Hubble's Law tells us that the universe is expanding, it also implies that in the past the universe was much smaller than it is today. If we assume that the expansion's apparent velocity (that is, how fast the galaxies appear to be moving apart) has been constant over the history of the universe, we can calculate how long ago the galaxies began their separation. This should tell us the time that the expansion began, which should give us an estimate of the age of the universe.

If the expansion of the universe is happening rapidly, then we expect the universe to be relatively young, because it has taken only a short time for the galaxies to expand to large distances. If, on the other hand, the universal expansion is progressing at a slow speed, then the age of the universe should be relatively old, because it has taken a long time for the galaxies to reach large distances from each other. We know how fast the universe is expanding, because we know the value of Hubble's constant (H0 ). The faster the universe is expanding, the faster the galaxies will appear to be moving away from each other.

You can actually calculate an estimate for the age of the Universe from Hubble's Law. The distance between two galaxies is D. The apparent velocity with which they are separating from each other is v. At some point, the galaxies were touching, and we can consider that time the moment of the Big Bang. If you take the separation between the two galaxies (D) and divide that by the apparent velocity (v), that will leave you with how long it took for the galaxies to reach their current separation. The standard analogy here is to consider that you are now 300 miles from home. You drove 60 mph the entire time, so how long did it take you to get here? Well, 300 miles / 60 mph = 5 hours.

  • So, the time it has taken for the galaxies to reach their current separations is t=D/v .
  • But, from Hubble's Law, we know that v= H 0 xD .
  • So,  t=D/ v=D/ ( H 0 ×D )=1/ H 0 . So, you can take 1/ H 0 as an estimate for the age of the Universe.
  • The best estimate for H 0 = 73km/ s/ Mpc . To turn this into an age, we'll have to do a unit conversion.
  • Since 1Mpc=3.08× 10 19 km , H 0  = ( 73 km/s/Mpc ) x (1 Mpc/3.08 x  10 19  km) = 2.37 x  10 18  1/s .
  • So, the age of the Universe is  t = 1/ H 0  = 1 / 2.37 x  10 18  1/s = 4.22 x  10 17  s = 13.4 billion years .

From stellar evolution, we have estimated the ages of the oldest globular clusters to be approximately 12-13 billion years old. These are the oldest objects we have identified, and it is a nice check on our estimates for the age of the Universe that they are consistent. It would have been strange if we were unable to find any objects roughly as old as the Universe or if we found anything significantly older than the estimated age of the Universe. For many years, until about 10 years ago, however, there was a controversy over the age of the universe derived from Hubble's Constant. The best theories available at the time were estimating that the stars at the Main Sequence Turn Off in many globular clusters had ages of 15 billion years old or more. This creates a problem. How can the universe contain an object older than itself? Recently, however, advances in our understanding of the stars have led us to refine the ages of the stars in globular clusters, and we now estimate them to be about 13 billion years old. This means, though, that the stars in the globular clusters must have formed within the first several hundred million years of the universe's existence!