If you browse either through popular science physics or through the most recent publications on the particle physics' preprint server arxiv.org then there is one topic which you cannot miss: Dark matter.
What is dark matter? Well, we do not know. So why do we care? Because we know something is out there, something dark, and its moving. Or, more precisely, it moves stuff around. When we look to the skies and measure how stars and galaxies move, then we find something interesting. We think we know how these objects interact, and how they therefore influence each other's movement. But what we observe does not agree with our expectations. We think we have excluded any possibility that we are overlooking something known, like that there are many more black holes, intergalactic gas and dust, or any of the other particles we know filling up the cosmos. No, it seems there is more out there than we can detect right now directly and have a theory for.
Of course, it can be that we miss something about how stars and galaxies influence each other, and this possibility is also pursued. But actually the simplest explanation is that out there is a new type of matter. A type of matter which does not interact either by electromagnetism or the strong force, because otherwise we would have seen it in experiment. Since there is no interaction with electromagnetism, it does not reflect or emit light, and therefore we cannot see it using optics. Hence the name dark matter. Because it is dark.
It certainly acts gravitationally, since this is how stars and galaxies are influenced. It may still be that it either interacts by the weak interaction or with the Higgs. That is something which is currently investigated in many experiments around the world. Of course, it could also interact with the standard model particles by some unknown force we have yet to discover. This would make it even more mysterious.
Because it is so popular there are many resources on the web which discuss what we already know (or do not know) about dark matter. Rather than repeating that, I will here write why I start to be interested in it. Or at least in some possible types of it. Because dark matter which only interacts by gravitation is not particularly interesting right know, as we will likely not learn much about in the foreseeable future. So I am more interested in such types of dark matter which couple by some other means to the standard model. Until they are excluded by experiments.
If it should interact with the standard model by some new force then this new force will look likely at first just like a modification of the weak interactions and/or of the Higgs. This would be an effective description of it. Given time, we would also figure out the details, but we have not yet.
Thus, as a first shot, I will concentrate on the cases where it it could interact with the weak force or just with the Higgs. Interacting with the weak force is actually quite complicated if it should fulfill all experimental constraints we have. Modifications there, though possible, are thus unlikely. Leaves the Higgs.
Therefore, I would like to see how dark matter could interact with the Higgs. Such models are called Higgs portal models, because the Higgs act as the portal through which we see dark matter. So far, this is also pretty standard.
Now comes the new thing. I have written several times that I work on questions what the Higgs really is. That it could have an interesting self-similar structure. And here is the big deal for me: The presence of dark matter interacting with the Higgs could influence actually this structure. This is similar to what happens with other bound states: The constituents can change their identity, as we investigate in another project.
My aim is now to bring all these three things together: Dark matter, Higgs, and the structure of the Higgs. I want to know whether such a type of dark matter influences the structure of the Higgs, and if yes how. And whether this could have a measurable influence. The other way around is that I would like to know whether the Higgs influences the dark matter in some way. Combining these three things is a rather new idea, and it will be very fascinating to explore it. The best course of action will be to do this by simulating the Higgs together with dark matter. This will be neither simple nor cheap, so this may take a lot of time. I will keep you posted.