## Tuesday, November 20, 2007

### A layman’s tutorial to the dark side II

In the previous post, we tried to answer the question “What is dark matter?” In this post, in the same reductionist spirit, we try to answer the question “What is dark energy?” [1]. For a number of years, I kept thinking that dark energy was just “E =mc^2” type energy associated with dark matter. It was only in my second year in grad school that I realized how hopelessly wrong I was.

As in the context of dark matter, dark energy is postulated to exist to solve some problems associated with explaining observed phenomena. So, first let us talk about what the problem is. The problem is that the universe is expanding and the rate of this expansion is increasing, i.e., the expansion of the universe is accelerating! The first question you might ask is “Are you sure?” or “How do we know this?” I do not want to discuss red shifts and the Hubble constant here. So I refer you to wikipedia for more info on this. What I would like to do here is to take as a given that the universe is expanding and accelerating and ask how can we understand this?

The theory of classical gravity is General Relativity. A layman’s minimal picture of what GR is with respect to the familiar Newtonian picture can be summarized quickly enough [2]. But, for the purpose at hand, it suffices to say that one of the consequences of GR is that matter and energy exert a pressure on space time much like a gas in a chamber exerts a pressure on the piston [3]. Now, suppose we use this piston analogy for minute. If I have gas under pressure, kept that way by putting a weight on the piston. I suddenly remove this weight and I ask you what you expect the motion of the piston to be like. You would tell me that the piston would first instantaneously accelerate to a large speed, then decelerate slowly as the gas in the chamber expands. Yes? This same picture is what you would expect to apply to the universe as well. You can think of the total mass and energy of the universe as N in some units. Suppose the volume of space time is V(t) at a given time t, then the pressure exerted by this mass and energy will be proportional to N/V. At the time of the big bang, i.e., t=0, this was enclosed in a very very small volume. Hence it must have exerted tremendous pressure and the universe must have expanded rapidly. As time increases, universe expands, V increases, N/V(t) decreases, and so the universe should expand more slowly than before. If this was the case, then there would be no problems and we would not have so many cosmologists so worried so much of the time.

But, observations of far away galaxies tell us that the universe is expanding faster than it was at earlier times! The question is, how can this be? Clearly, it cannot be from the regular mass and energy that we talked about earlier. So we have to think of something else. One of the possible “something else” is that there is an (as yet mysterious) energy associated with space time itself. If this was the case, then as the universe expands, the number of space time points increases in some sense. Then, this intrinsic energy associated with the space time points increases as well and so the pressure builds up and the universe expands faster. So, the existence of such an energy, the dark energy, could be one possible explanation for the accelerating universe. But where the heck does this energy come from? We have no clue at the present time. Hence the name dark energy.

[1] A more complete and erudite discussion is here.

[2] This is fishing. If you ask me, I will tell you kind of thing.

[3] I know that relativist cringe at such statements, but I do not see how else to say this simply.

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