Future of the Universe

Think about a rocket fired upward from the earth. At launch it is given a large speed, and because of this initial speed its distance from the earth keeps growing. But the earth's gravity pulls on it the whole time, so its speed keeps falling. Something else is happening as well. Gravity becomes weaker as the distance between two bodies increases. So as the rocket climbs, the very force that is slowing it down is itself getting weaker.

So two things are shrinking together: the rocket's speed and the pull of gravity on it. What happens next depends on which of the two reaches zero first. There are only three possibilities:

• (a) If the effect of gravity becomes zero while the rocket still has some speed, nothing is left to pull it back. The rocket keeps moving away from the earth forever.
• (b) If the speed of the rocket becomes zero while gravity is still acting, the rocket stops for a moment and is then pulled back. It falls towards the earth.
• (c) If the effect of gravity becomes zero at exactly the moment the speed becomes zero, the rocket neither moves on nor falls back. It stays where it is.

The whole universe behaves like that rocket, on an enormous scale. All the galaxies are moving away from each other at a certain velocity, and the size of the universe is increasing. At the same time, the gravitational pull of all the masses in the universe acts on every galaxy, so the velocity of the galaxies is slowly decreasing. As the galaxies spread farther apart, the effect of gravity between them decreases too.

So the universe faces the rocket's question. Will the velocity of the galaxies become zero before the effect of gravity does? Will gravity become zero before the velocity does? Or will both become zero at the same time? The answer determines the future of the universe. The three answers give three kinds of universe: open, flat and closed.

How strong gravity is comes from Newton's universal law of gravitation. According to this law, every mass exerts a gravitational force on every other mass, and they pull each other towards themselves. The magnitude of the force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres:

\[ F = \frac{G\, m_1 m_2}{d^2} \]

Here \( m_1 \) and \( m_2 \) are the two masses, \( d \) is the distance between their centres and \( G \) is the universal gravitational constant. Two things follow for a galaxy. The more mass there is in the universe, the stronger the total pull on it. If that same mass is spread through a larger volume, the distances grow and the pull becomes weaker. So the net gravitational force on any celestial body depends on the total mass in the universe and on the volume of the universe.

Mass and volume can be joined into one quantity. The ratio of mass to volume is called density:

\[ \rho = \frac{M}{V} \]

Here \( \rho \) is density, \( M \) is mass and \( V \) is volume. For the whole universe we use its average density: the total mass of the universe divided by its total volume. So the net magnitude of the gravitational force depends on the average density of the universe. The higher the average density, the stronger the gravity holding the galaxies back.

Since gravity is set by the average density, there must be one particular value of density that is just enough to stop the expansion. This value is called the critical density. If the expansion of the universe ever stops, it could happen only after billions of years.

Comparing the actual average density of the universe with the critical density tells us which future the universe will have:

• Average density less than the critical density: gravity cannot stop the expansion, and the universe is open.
• Average density equal to the critical density: the expansion slows down and finally stops, and the universe is flat.
• Average density greater than the critical density: gravity stops the expansion and pulls the universe back together, and the universe is closed.

Suppose the celestial bodies still have some velocity left when gravity becomes zero. Then no force remains to stop them. They continue to move away from each other forever, and the size of the universe keeps increasing. This is like the first case of the rocket, where the rocket never comes back.

In terms of density: if the average density is less than the critical density, there is not enough mass in the universe to hold the expansion back. Gravity cannot hold the expanding process, so the universe that is continuously expanding now will continue to expand in the future too.

What if gravity and the velocity of the celestial bodies become zero at exactly the same time? After that there is no motion carrying the bodies onward and no force pulling them back. The celestial bodies remain in the same positions and the universe remains stable. This matches the third case of the rocket, where the rocket stays where it is.

If the average density is equal to the critical density, the expansion rate of the continuously expanding universe gradually decreases and finally stops. By then the distance between each celestial body has become infinitely large. At such a distance they are not affected by their mutual gravitational force, so they do not start coming back together.

Now think of the opposite case. If the gravitational effect is still nonzero when the velocity of the celestial bodies becomes zero, the bodies stop for a moment and gravity begins to pull them towards each other. They come closer and closer, and in the end the whole universe comes to a single point. This matches the second case of the rocket, where the rocket falls back to the earth. It happens when the average density of the universe is greater than the critical density.

If the Big Crunch happens, the universe that was created by the explosion of a single point will end up as a point again, and that point may explode once more to form a new universe like the present one. This means that, just like the life cycle of a star, the age of the universe is fixed and the universe also has a life cycle. For this cycle to continue, the Big Bang and the Big Crunch must keep happening in turn:

• Big Bang: a single point explodes and the universe begins.
• Expansion: the galaxies move apart and the universe grows.
• Slowing: gravity reduces the velocity of the galaxies.
• Stopping: the velocity becomes zero while gravity is still acting.
• Contraction: gravity pulls the galaxies back together.
• Big Crunch: the whole universe collapses to a single point.
• New Big Bang: that point explodes again and a new universe forms.

These facts can be shown on a single graph. The horizontal axis shows the time since the Big Bang and the vertical axis shows the radius of the universe. All three curves start from the same point, because all three universes begin with the Big Bang. After that they separate.

• The open universe curve keeps rising. The universe goes on expanding.
• The flat universe curve rises, but more and more slowly, and finally levels off. The expansion slows and stops.
• The closed universe curve rises to a peak, then falls back down to zero. That point is the Big Crunch.

The open, flat and closed universes are named according to the nature of these graphs. The main factor that determines the future of the universe is gravity, and the magnitude of gravity depends on the mass and size of the universe, that is, on its density.

To know whether the universe is open, flat or closed, we need to know its average density. The density of the universe is estimated from the masses seen in space. The masses of the stars, galaxies and clouds of gas seen through telescopes are added up and compared with the volume they occupy, which gives an estimate of the density.

This is not easy. The universe is enormous and we can see only part of it. Some matter gives out no light, so it cannot be seen directly. So the present value is only an estimate. More powerful telescopes and new technology may make the estimate more accurate in the future, and only then can the future of the universe be predicted with more confidence.