Go look at the last 12 or so slides in this presentation. I hope this will be released soon – it should be fun to play around with. I am especially interested to see how it works out the problem of finding invariants in general tensor products of Lie group representations. At this point I am not sure how to do this in an algorithmic manner. After seeing the slides, I was inspired to write a short Mathematica function that finds the terms of a given dimension allowed by some collection of scalar fields with different U(1) charges. This was relatively easy – the hard part would be finding all the independent singlets of, for example, SU(2) that can then be formed once the U(1) constraint is satisfied. Automatically generating the terms in, for example, the Higgs potential in this paper, would be impressive.
And here is the mandatory comment on BICEP2: I don’t understand inflationary physics nearly well enough to offer anything original – and if I did, I would probably be writing a paper on it right now.