Spontaneous symmetry-breaking lies at the heart of the analogy – graphene loses some symmetry in the transition from a flat shape to a rippled one, in the same way as the "activation" of the Higgs field is tied to the breaking of the electroweak symmetry. Compared with grand cosmological scales, sheets of carbon might seem a bit pedestrian, but San-Jose thinks otherwise. "Measuring the rippling of graphene under variable tension could give us information about the details of the intrinsic condensation of the Higgs," he says.
This is another example where condensed matter systems can provide important and fundamental information in physics. It is why I've always argued that condensed matter physics isn't JUST "applied physics". It is why systems such as the newly-discovered topological insulators are so fascinating and so rich. There are some very fundamental physics that can be studied and tested in such systems.
 P. San-Jose et al., Phys. Rev. Lett. v.106, p.045502 (2011).