Reconstructing Inflation

All sorts of responsibilities have been sadly neglected, as I've been zooming around the continent -- stops in Illinois, Arizona, New York, Ontario, New York again, and next Tennessee, all within a matter of two weeks. How is one to blog under such trying conditions? (Airplanes and laptops are involved, if you must know.) But the good news is that I've been listening to some very interesting physics talks, the kind that actually put ideas into your head and set off long and convoluted bouts of thinking. Possibly conducive to blogging, but only if one pauses for a moment to stop thinking and actually write something. Which is probably a good idea in its own right. One of the talks was a tag-team performance by Dick Bond and Lev Kofman, both cosmologists at the Canadian Institute for Theoretical Astrophysics at the University of Toronto. The talk was part of a brief workshop at the Perimeter Institute on "Strings, Inflation, and Cosmology." It was just the right kind of meeting, with only about twenty people, fairly narrowly focused on an area of common interest (although the talks themselves spanned quite a range, from a typically imaginative propsoal by Gia Dvali about quantum hair on black holes to a detailed discussion of density fluctuations in inflation by Alan Guth). Dick and Lev were interested in what we should expect inflationary models to predict, and what data might ultimately teach us about the inflationary era. The primary observables connected with inflation are primordial perturbations -- the tiny deviations from a perfectly smooth universe that were imprinted at early times. These deviations come in two forms: "scalar" perturbations, which are fluctuations in the energy density from place to place, and which eventually grow via gravitational instability into galaxies and clusters; and the "tensor" perturbations in the curvature of spacetime itself, which are just long-wavelength gravitational waves. Both arise from the zero-point vacuum fluctuations of quantum fields in the very early universe -- for scalar fluctuations, the relevant field is the "inflaton" φ that actually drives inflation, while for tensor fluctuations it's the spacetime metric itself. The same basic mechanism works in both cases -- quantum fluctuations (due ultimately to Heisenberg's uncertainty principle) at very small wavelengths are amplified by the process of inflation to macroscopic scales, where they are temporarily frozen-in until the expansion of the universe relaxes sufficiently to allow them to dynamically evolve. But there is a crucial distinction when it comes to the amount of such fluctuations that we would ultimately see. In the case of gravity waves, the field we hope to observe is precisely the one that was doing the fluctuating early on; the amplitude of such fluctuation is related directly to the rate of inflation when they were created, which is in turn related to the energy density, which is given simply by the potential energy V(φ) of the scalar field. But scalar perturbations arise from quantum fluctuations in φ, and we aren't going to be observing φ directly; instead, we observe perturbations in the energy density ρ. A fluctuation in φ leads to a different value of the potential V(φ), and consequently the energy density; the perturbation in ρ therefore depends on the slope of the potential, V' = dV/dφ, as well as the potential itself. Once one cranks through the calculation, we find (somewhat counterintuitively) that a smaller slope yields a larger density perturbation. Long story short, the amplitude of tensor perturbations looks like