There has been discussion among cosmologists about galileons, a hypothetical class of effective scalar fields which are extremely universal and arise generically in describing the short distance behavior of the new degrees of freedom introduced during the process of modifying gravity, and in describing the dynamics of extra dimensional brane worlds.  They might be able to explain dark matter - no cosmological constant needed.

Despite prolific use of the term 'theory', they are math that hopes to become physics.

Modified gravity and brane worlds are just some of the ideas that have been studied as possible solutions to the cosmological constant problem — the problem of explaining why our universe seems to be accelerating. Galileons possess non-trivial symmetries, and are well behaved quantum mechanically compared to other types of fields.

In a new paper, authors investigate whether it is possible to extend the key symmetries of the galileons even further, by enlarging the set of transformations under which the hypothesis remains invariant. It is found that while it is not possible to enlarge this symmetry while maintaining the symmetries of special relativity and not introducing new degrees of freedom, it is possible to create new kinds of Galileon-like theories it the system is non-relativistic.

Non-relativistic systems such as superfluids are described by effective degrees of freedom known as Goldstone bosons. Goldstone bosons are manifestations of spontaneous symmetry breaking, where the symmetries of a system are not realized by its ground state.

The new kinds of Galileon-like hypotheses uncovered here could be useful as descriptions of systems near Multi-critical points, points in the phase diagram where multiple phases coincide, the authors believe.

Citation: Kurt Hinterbichler, Austin Joyce, 'Goldstones with extended shift symmetries',  International Journal of Modern Physics D July 1 2014 DOI: 10.1142/S0218271814430019. Source: World Scientific