Inflation II
In the

last post we talked about inflationary cosmology, the density perturbations it predicts, and how these perturbations show up in the cosmic microwave background (not to mention in the large-scale structure of galaxies today).

If this story is true, properties of the universe during the inflationary era are reflected (albeit faintly) in properties of the perturbations. For example, the overall amount of perturbation

*A* (which is one part in 100,000) is related to the energy density of the universe during inflation; unfortunately it's also related to another number, the "slow-roll parameter" ε (epsilon), which describes how the rate of inflation gradually slows with time. (Have to be a bit technical here, sorry.) Roughly, the energy scale

*E*_{I} of inflation (the number which, when raised to the fourth power, is the energy density during inflation) obeys

*E*_{I} = *A*^{1/2} ε^{1/4} *E*_{P}.

Here,

*E*_{P} is the Planck scale, the magical energy at which quantum gravity is supposed to become important:

*E*_{P}=10

^{18} billion electron volts. (A billion electron volts is one GeV, "G" for "giga-". The rest energy in a single proton, via

*E=mc*^{2}, is about 1 GeV.) For comparison, the highest energy yet probed by particle accelerators here on Earth is about a trillion electron volts, smaller than the Planck scale by 10

^{-15}. Accessible experiments are not going to tell us anything directly about energies as high as the Planck scale; cosmology might be our best hope for learning something empirical about quantum gravity. For more details about inflation and perturbations you can look at a technical introduction to inflation by

Andrew Liddle.

Let's plug in numbers. The perturbation amplitude

*A* is 10

^{-5}. The slow-roll parameter ε is supposed to be small, perhaps 10

^{-2}; but we're taking the fourth root, so we'll end up with something of order unity. This means that the energy scale of inflation

*E*_{I} appears to be of order 10

^{15}-10

^{16} billion electron volts. This is intriguing, since this scale is right where we expect to have

grand unification -- the coming-together of the three major forces in the universe other than gravity (electromagnetism, the strong nuclear force, and the weak nuclear force).

Could this be a coincidence? Sure. We certainly haven't been very precise, to say the least. But an optimist would see hints of a consistent picture forming, in which the physics of grand unification is somehow behind the phenomenon of inflation. It's by no means a complete theory, but an encouraging tidbit that is worth pursuing. Theorists will look for specific models of inflation, while experimentalists will look for new ways to test its predictions. Unfortunately, there aren't that many predictions. One is that the overall geometry of space is very close to flat; this has been spectacularly confirmed by observations of the microwave background and elsewhere. Another is that the fluctuations in density should be accompanied by independent fluctuations of the gravitational field (gravitational waves), which leave a distinctive signature on the polarization of the microwave background. Looking for such a signal is a big goal of cosmologists right now.

Meanwhile, the fact that the energy scale of inflation seems to be tantalizingly close to the Planck scale leads people to wonder whether we can't see explicit effects of quantum gravity in the CMB. It's hard to give a definitive answer to this question, just because we don't really know what the explicit effects might be. They might, for example, cause the perturbations to deviate from perfectly uniform behavior on all scales, perhaps by imprinting a tiny oscillating variation. But right now there's little consensus about this quantum gravity/inflation connection; we have a ways to go before making it into something concrete.