Chapter 17: Cosmology

In understanding the universe, we face limitations of space and time. One important consequence of relativity is that space and time are linked; Einstein talked of a space-time continuum. We have already seen evidence of this in cosmology. Since light takes a long time to reach us from distant objects, we see them as they were at a younger age. Although our examples use light, the discussion applies to all electromagnetic waves, including radio waves, X-rays, and so on. It makes no sense to ask what a quasar looks like "now." Information cannot be transmitted instantaneously in the universe, so we are limited in our knowledge by the finite speed of light. Looking out in space means looking back in time.

Past and future relative to the origin. For the grey areas a corresponding temporal classification is not possible.

A simple space-time diagram.

A space-time diagram is a graphical way of showing evolution in time and space. For simplicity, the three dimensions of space are collapsed into one. Astronomers use the scale factor, R, to describe the size of the universe. By convention, space is plotted horizontally and time is plotted vertically, increasing upward. If you think space-time diagrams sound esoteric, some everyday examples will show that every meeting or interaction must be specified both in space and time. Suppose you plan to meet a friend for lunch. The two ways you might miss your appointment are by going to the right place but getting the day wrong or by going to the wrong restaurant at the right day and time. In other words, you must consider both space and time to make an appointment. Suppose that you are trying to catch a fly ball in baseball. You might miss the catch either by getting to the place the ball lands too late or by misjudging the flight of the ball and running to the wrong place. Once again, a successful catch requires space and time to be considered together.

The finite speed of light imposes limitations in a space-time diagram. Imagine that a supernova has just exploded at position A. It will take a time T_A for the light from the supernova to reach us. If A is 0.3 parsecs away, it will take just under a year to see the first light of the supernova. Other events at larger distances B and C will take longer times T_B and T_C to be seen by us. Since nothing can travel faster than light, we cannot know about the supernova as it is now — that would require the instantaneous transfer of information. All we can do is wait a year for the information from A to reach us, and then wait even longer times for information from B and C to reach us.

Now imagine that you are located at A and you start observing the universe at time zero. At that same time, supernovae explode at positions B and C, remote from you in space. As time goes by, the light from those events travels through space. But it is not until time T_A that the supernova at point B becomes visible to you. The supernova at point C takes even longer to reach you (a time 2T_A, if the distance from A to C is twice the distance from A to B). The region of space within which you can observe events that occurred since time zero grows steadily. Astronomers call this region of space the horizon. We can know nothing about regions of space that lie outside our horizon.

The concept of a horizon leads to some bizarre consequences of the big bang model. Since the expansion has been decelerating until recently, space was expanding more rapidly in the past. The current expansion rate is given by the Hubble constant. The present-day value of the Hubble constant is the same everywhere in space — in other words, the linear Hubble relation applies at all distances — just as we would expect from the expanding balloon analogy. However, there was a time in the past when space was expanding faster than the speed of light! The speed limit of c imposed by the special theory of relativity only applies on local scales. (For the same reason, it is inappropriate to use the Doppler Effect to describe cosmological redshifts.) On the global scales described by the general theory of relativity, space can be expanding at any speed. The expanding universe has no speed limit!

The point in the past when the universe was expanding at the speed of light corresponds to a redshift of z = 1.25 and a time about 5 billion years ago when the universe was 40 percent of its current size. (These numbers depend on the cosmological model, we have chosen flat space-time for this illustration.) In other words, when the light from a galaxy or quasar at z = 1.25 was emitted, that object was moving away from us at the speed of light. Since then, the expansion has slowed (and more recently, speeded up due to dark energy) and photons have been able to traverse the large distance between the object and us. The most distant quasars have z = 7 and the most distant galaxies have z = 11. This second redshift corresponds to a time about 13.5 billion years ago when the universe was 3 percent of its current age. When the light we see from a distant quasar was emitted, it was moving away from us at nearly five times the speed of light! Thus, space was being created so rapidly that not only the quasar but also the photons it emitted were being "dragged" away from us by the expansion. Our intuitive notions of light travel time also come unstuck. In the local universe, light from a star one light-year away takes one year to reach us. Light from a galaxy a million light-years away takes a million years to reach us. But light in an expanding universe has to struggle to overcome the expansion. That is why the most distant objects in a universe 13.8 billion years old can be 25 billion light years away and the edge of the visible universe can be 46 billion light years away.

Extreme situations call for extreme analogies. Imagine that your top running speed is the speed of light. Now imagine that you are talking to a friend at the end of a long, moving sidewalk at an airport. Suddenly the sidewalk starts moving rapidly, carrying you away from your friend. That situation represents the big bang. Space is being "created" between you and your friend. You put your bag down and run — your bag is the quasar and you are the photon it emits. Initially, the sidewalk is moving so fast that, even when you run as fast as you can, you are carried away from your friend. That scenario is analogous to the early universe. After a while, the moving sidewalk slows down and you begin to approach your friend — a situation representing the universe at half its present age. By the time you reach your friend the sidewalk has slowed to a crawl and you reach your friend at full tilt (the speed of light), a much faster speed than the moving sidewalk is traveling. Meanwhile, your bag (the quasar) is far behind you, carried off by the expansion of space.

As time passes, larger and larger regions of the universe become visible. The steadily growing boundary of the observable universe is our horizon. Since there is no center to the expansion, we see out in space and back in time in every direction we look. As time goes by, light from more and more distant objects reaches our telescopes — we say the objects "enter our horizon". The observable universe grows a little larger each day. We can now see the distinction between the observable universe and the physical universe. Since the early expansion was faster than the speed of light, there are regions of space we have never seen. An open universe is infinite in size, but the observable universe is limited to the regions from which light has had time to reach us. Dark energy throws a big new wrinkle on this picture. Accelerating expansion means that regions that are within our horizon now will one day be moved beyond our horizon. Galaxies that we can see now will not be visible forever. Some day they may all be removed from our view. Astronomers should enjoy the extragalactic universe while they can!