The Ageof 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. Thus, the age of such clusters place a limit on the age of the Universe, for it must be at least as old as the objects that it contains. Such estimates typically yield ages in the range 14-18 billion years

## Hubble Time

The inverse of the Hubble constant H has the units of time because the Hubble law is

v = H d

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 (e.g., if I travel 180 miles at 60 miles/hour, the time required is t = d/v = 180/60 = 3 hours).

Thus, the Hubble time T is just the inverse of the Hubble Constant:

T = 1 / H

Taking a value of H = 20 km/s/Mly (where Mly means mega-light years),

where all the factors are necessary to convert the time units to years and I've rounded some numbers to simplify the display.

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. The Hubble "constant" actually isn't constant, so the Hubble time is really only a rough estimate of 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 16 thousand million years), while a larger value of 80 km/s/Mpc gives a lower value for the age (around 10 thousand million 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 15 billion years for the Universe.

### The Fate of the Universe

The Universe is currently expanding. One extremely important cosmological question is whether this expansion will continue forever. As we shall see later, this is a question that does not yet have a definitive answer. Ultimately, this will turn out to be a question of how much mass is contained in the Universe. If it is below a critical amount, the Universe will expand forever. If it is above the critical amount, the expansion will eventually reverse and the Universe will collapse on itself, leading to what has been termed the big crunch. If it is exactly equal to the critical amount, the expansion will slow, but will only stop after an infinite amount of time. Thus, in this case the Universe will expand forever too.

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