I'm not an expert on the Voyager missions, but as a theoretical particle physicist/cosmologist I can tell you that nobody really expects the Voyager probes to discover anything "fundamental" in these fields. We've already got a rough idea of what the interstellar medium (ISM) is like from numerous astronomical observations (I'm sure an astronomer could tell you more), and basically the energy scales are too small to probe the sort of new physics that, for example, the LHC explores. On the other hand the energy scales are too large to probe the sort of frontier that cosmology explores. So the ISM is well in the range of physics we think we understand.
There is a small chance that the Voyager probes could discover something like MOND, if careful tracking of their orbits does not follow our understanding of gravity. For a long time (certain) people thought this might be the case for the Pioneer anomaly, but very careful studies of the solar heating of the spacecraft showed that the anomaly was mundane - only a misunderstood systematic error, not new physics. So it is conceivable but very unlikely, along both theoretical and experimental lines, that the Voyager probes could discover modified gravity. If it does happen then that will be tremendously exciting!
Hopefully an astronomer will come on here and tell you what they do expect to learn from Voyager. Presumably something about the conditions of the ISM.