Fermi, the telescope formerly known as GLAST, has been used to bring us many new insights, confirmations, and perspectives on physical phenomena. It turned out that it was a damn good idea to look at our cosmic environment using new eyes that are sensitive to gamma rays.
You must realize that the gamma rays heavily interact with the atmosphere which pollutes the message they carry in space which is why it was such a new idea to look for gamma rays in outer space. A great investment of $0.69 billion dollars: compare with various bailouts or hundreds of billions wasted for a "fight against climate change".
Among the jobs done by Fermi, recall that we have discussed the positrons produced by lightnings, falsification of Lorentz-breaking theories, new hints for a hypothetical yet speculative WMAP haze. And I haven't even discussed many details about the gamma ray bursts that the astrophysicists surely find useful.
However, Softpedia presents a hep-ph preprint that offers a possible future job to Fermi. It connects the telescope with another, seemingly unrelated player in physics: the Higgs boson:
Jackson, Servant, Shaughnessy, Tait, Taoso: Higgs in space!The five authors discuss the possibility that the Fermi telescope could actually discover the God particle before the LHC will! If the dark matter WIMP particle is linked to the electroweak symmetry breaking (and it's the case e.g. in the Randall-Sundrum inspired models where WIMP is a kind of a relatively light right-handed neutrino), and it's the main "If" in this argument, its annihilation could produce a new virtual Z^prime-boson that could decay either to two photons or, via a top-quark loop, to a photon and a Higgs boson! Such channels would leave pretty discernible patterns in the observed gamma ray spectrum, as seen by Fermi. (Parts of the parameter space of this possibility have already been excluded by Fermi.) The preprint is mostly dedicated to these fingerprints.
I find the conditions needed for these fingerprints to materialize in reality to be "less likely than yes" (or whatever is the opposite to "more likely than not": I want to say that the probability is below 50%) but such a scenario is not quite inconceivable and it would surely be fascinating to see the God particle in the skies although most of us expect Him to reside deeply in the souls of ourselves and of our terrestrial colliders. ;-)