Exam nightmares

The students in my cosmology course had their exam last week.

There’s no doubt that they found the course tough this year — it was my first time teaching it, and I departed pretty significantly from the previous syllabus. Classically, cosmology was the study of the overall “world model” — the few parameters that describe the overall contents and geometry of the Universe, and courses have usually just concentrated upon the enumeration of these different models. But over the last decade or two we’ve narrowed down to what is becoming a standard model, and we cosmologists have begun to concentrate upon the growth of structure: the galaxies and clusters of galaxies that make the Universe interesting, not least because we need them for our own existence. Moreover, that structure directly teaches us about those contents which make them up and the geometry in which they are embedded. I wanted to give the students a chance to learn about the physics behind this large-scale structure, not traditionally at the heart of undergraduate cosmology courses.

Unfortunately, this also meant that the traditional undergraduate textbooks didn’t cover this material at the depth I needed, and so the students were forced to rely on my lectures and the notes they took there (and eventually a scanned and difficult-to-read copy of my written notes).

I sensed a bit of worry in the increasing numbers of questions from students in the weeks before the exam, and heard rumors of worries. But the day of the exam rolled around, and indeed when I re-read the questions it didn’t seem too bad, although there were some grumbles evident in the examination room.

Later I learned that there was a “record-breaking” number of complaints about the exam. I gather it was perceived to be difficult and unfamiliar.

So marking the exams in the past week, I was happy to find that the students performed just fine: the right “bell-shaped curve”, the correct mean, etc. (Of course I should point out that all results are subject to final approval by the Physics Department Examiners Committee.) I admit some puzzlement, therefore, about the reaction to the exam. Were they worried because the questions were different from those they had seen before? That, I admit, was the point of the exam — to test if they have actually learned something. Which, I am happy to point out, it seems that they had!

There was one question that almost all students got wrong, however. I asked about the “Cosmological Constant Problem” and whether it could be solved by the theory of cosmic inflation. The Cosmological Constant is a number that appears in General Relativity, and, although we can’t predict it for certain, we are pretty sure that if it’s not strictly zero, in most theories we would estimate that it ought to have a value something like 10120 (that is 1 followed by 120 zeros!) times greater than that observed in the Universe today. I suppose I didn’t write on the board the words “Cosmological Constant Problem” next to that extraordinarily large number. (In the end, I reapportioned the small number of marks associated with that problem.) Inflation involves something very much like the cosmological constant, but occurring in the very early Universe — so inflation can’t help us with the 120 zeroes, alas.

Next year, I’ll be sure to spell all of this out, but I’ll also show this movie of my old grad-school friend, collaborator, and colleague Lloyd Knox, now a professor at the University of California, Davis, singing this song about Dark Energy (of which the cosmological constant is a particular manifestation):

The scientifically-accurate lyrics are sung to the tune of Neutral Milk Hotel’s “In the Aeroplane over the Sea”.

Finally, I’d welcome comments on the course or the exam, anonymous or otherwise, from any students who may come across this post.