Age of the Universe

As we shall discuss further in connection with the big bang, there is strong evidence that the Universe has not always existed, but instead came into being a finite amount of time ago. There are several measures of the age of the Universe. Let us discuss two: (1) the age of globular clusters and (2) the inverse of the Hubble constant.

Globular Clusters

As we have already discussed, the turn-off point for the HR diagram in globular clusters provides a measure of the age of the cluster. The figure below, reproduced from Chapter 19, illustrates. The ages of such clusters place a limit on the age of the Universe, for the Universe must be at least as old as the objects that it contains. Some earlier estimates typically yielded ages in the range 14-18 billion years for globular clusters, which exceeded the age of the Universe in some estimates and therefore led to a logical contradiction.

As we have noted in our earlier discussion of parallax measurements in Chapter 18, revisions of the distance scales due to Hipparcos parallax measurements, coupled with revisions of stellar evolution models that relate age to turn-off point, have lowered these estimated ages by significant amounts. Now we believe that the globular clusters of our galaxy have ages in the range of 11 to 13 billion years, which removes much of any potential discrepancy with other estimates of the age of the Universe unless the Hubble constant is near the upper part of the range expected for it (see below).

Technically Speaking: The Inverse Hubble Constant
The inverse of the Hubble constant H has the units of time because the Hubble law is v = Hd, where v is the velocity of recession, H is the Hubble constant, and d is the distance. Thus, from this equation, we have that

1/H = d/v
But d/v is distance divided by velocity, which is time (for example, if I travel 180 miles at 60 miles/hour, the time required is t = d/v = 180/60 = 3 hours). So the inverse of the Hubble constant measures a time.

The Hubble Time

As demonstrated in the adjacent box, the inverse of the Hubble constant is a time, but what is the meaning of this time? We can think of it in the following way. The Universe is presently expanding. Imagine reversing the expansion so that it became a contraction and ran backwards. The physical interpretation of the Hubble time is that it gives the time for the Universe to run backwards to the big bang if the expansion rate (the Hubble "constant") were constant. Thus, it is a measure of the age of the Universe (but only approximately so, as discussed in the right panel). We find it useful then to define the Hubble time T as just the inverse of the Hubble constant:

T = 1 / H

From our discussion above, this time is closely related to the age of the Universe. Reasonable assumptions for the value of the Hubble constant and the geometry of the Universe typically yield ages of 10-20 billion years for the age of the Universe. For example, H near 50 km/s/Mpc gives a larger value for the age of the Universe (around 15 billion years), while a larger value of 80 km/s/Mpc gives a lower value for the age (around 10 billion years). Therefore, we shall take this information, and additional information from other methods to estimate the age of the Universe that we have not discussed, to indicate an age of approximately 10-15 billion years for the Universe.