For the last two days, NYU undergrads Ekta Patel and David Mykytyn have been doing great work on a range of projects. Patel has been working on visualizing and vetting the galaxies that make up the Sloan Atlas of Galaxies. This takes serious judgement and patience! Mykytyn has been quantitatively comparing the g and r fluxes of time-variable quasars, on a path to making a statistical model for arbitrarily heterogeneous multi-band, multi-epoch quasar photometry.
This morning, Jonathan Whitmore (Swinburne) gave a nice talk about monitoring the fine-structure constant (alpha) as a function of cosmic time using metal-line absorption in quasar spectra. He finds no signal (contrary to some claims in the literature) and has a plausible explanation for some weak claims: The detailed wavelength calibration of the echelle spectrograph he is using seems to be different for the arc calibrations and for the gas-cell (or solar analog) spectra. This might be because the arc illuminates the spectrograph very slightly differently than the astronomical source. He has to build a working model of all this if he wants to improve the precision of the experiments, which all seem to be limited by these kinds of issues at the present day.
It might all sound crazy, but in fact most current models of inflation or the vacuum energy density do generically predict fundamental-constant variations. They aren't that specific about magnitudes of fluctuations within the Hubble Time, but the predictions are there qualitatively.
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