Dark Energy: The Final Exam

Where do theoretical physicists get their ideas? That's a hard question to answer. But in the case of my most recent paper, which just appeared in Physical Review D (the preprint version is available here), I can tell you exactly where the idea came from: a final exam.

We're still trying to understand the exact nature of dark energy, which is driving the universe to expand faster every day. To try to bring some coherence to the discussion, cosmologists label the dark energy with a parameter called w, which describes the relation between the pressure of the dark energy and its density. And w also determines how the dark energy evolves with time. For ordinary matter (the stuff we're made up), w is zero, and the density of ordinary matter decays inversely as the cube of the expansion factor. Think of an expanding box filled with matter. As the box expands, the volume goes up as the cube of the size of the box, and the amount of matter stays the same, so the density goes down as the cube of the expansion.

We know from observations that the density of the dark energy stays nearly constant as the universe expands -- this corresponds to w close to -1. If w is exactly equal to -1, then the density is exactly constant, which corresponds to the famous "cosmological constant." You might think (and I did think) that if w were taken to be very close to -1, then the density of the dark energy would get closer and closer to a constant.  But your intuition would be wrong. It turns out that there are two different types of behavior possible in this case -- the density can go to a constant, just like the cosmological constant, or it can decay away to zero.

But how did I stumble upon this idea? I taught an undergraduate cosmology class last year and accidentally put a problem on the final exam in which w evolved to -1, but the density did not evolve to a constant. I puzzled over this as I graded the final exams and decided to look into it later in more detail. And it turned to be more interesting than I had possibly imagined. So teaching and research really are complementary activities -- not opposed to each other as people sometimes think.