There are two controversial theories I often write about here: The first, The Axial Force, a force possible between neutrinos which have opposite charges on left and right handed particles. Matter or anti-Matter doesn't seem to matter to the axial force. This follows from the CPT theorem. Combining the three operations, C (swapping matter and anti-matter), P (swapping left and right), T (reversing the direction of time, or equivalently the velocities of all particles), must result in no change to any picture of what has happened. Since most diagrams of an interactions are inverted by time reversal, either C or P but not both are also reversed. I've documented the Axial force in the paper linked from my blog, written here often about its consequences. As far as I know I'm the only current active researcher in the axial force, although the idea may date back to the 1970s. I happen to think the axial force will lead to a good theory of dark energy.
The second theory I often report on is Mirror Matter. Mirror Matter theory, posits a second of copy of mirror versions of all the known particles. Its was introduced because of the bizarre fact that weak nuclear force, between known particle, always acts in a left handed fashion. If there is a righted handed weak force its force carrier is very heavy, to heavy to have been observed. Mirror Matter solves restores the symmetry because its weak force is right handed. The theory also gives a good candidate of dark matter and fitting in with the recent observations from DAMA, COGENT. There are a number of researchers working on Mirror Matter, although only a minority, including Robert Foot and Paulo Cirarcelluti
So what happens between the two theories, are they compatible, indeed do they together lead to further explanations of the universe? Assuming both the axial force and mirror matter are real, we have eight copies of every particle, Matter versus Anti-Matter, Left-Handed versus, Right-Handed, and Mirror versus Ordinary Particles. The Known forces are also copied, with an electromagnetic force, and an mirror-electromagnetic force. Because the mirror-electromagnetic force is invisible to ordinary particles, dark matter stays dark. Is they're a also a mirror axial force. Quite possibly, if the standard model plus axial force, works, then so would a mirror copy. But what more interesting if you combine the axial and the mirror axial force, you can mixed them produce two copies, A+A' and A-A'. We may assume that A-A' breaks and gains an mass, while the total axial force remains massless. If in ordinary matter right handed neutrinos are heavy, then in the mirror world left handed neutrinos are heavy. If the heavy neutrinos and mirror neutrinos are bound by some interaction to a heavy composite particle, this is exactly the breaking we'll see. We'd also see a split in mass between to the ordinary light neutrinos and they mirror partners, these could also would mix, to form a very light set of neutrinos and a second set in the keV range, that would decay down to the lightest version.
A Consequences of add the axial force to the mirror matter model is then, we'd see only 3 light neutrinos at the time of nucleosynthesis, saving mirror matter theory from over counting the light of masses number of degrees of freedom, as reported below.
One problem with the mirror matter theory is that although mirror and ordinary matter may both make up a galaxy, when it comes to individual stars or planets we don't seem to see mixed objects containing varying amounts of each. What separates the two forms of matter> Gravity should attract both equally. I have thought of an effect, that would lead to the separation of ordinary and mirror matter. Imagine a collapsing cloud of gas, containing a mix of ordinary and mirror matter in some proportion. As it condenses it will be resisted by the Fermi pressure of the neutrinos needed to cancel out the axial force of the most populous gas (normal or mirror), at some stage the Fermi energy will rise above the mass of the a sneutrino or vectrino (a light supersymmetric boson carring the axial force), at this stage the gas will pair produce the vectrinos the with the opposite charge to the most populous gas which will rapidly condense, the vectrinos matching the less populus gas will stream out of the area carrying the less populous gas with it. This would lead to visible outflows of gas in interstellar clouds forming stars. These are indeed observed, even from area with no visable protostar, and called Herbig-Haro objects.
The shared axial force also helps explaining the different proportions of mirror and ordinary matter. Observation show that there is four to five times as much dark matter as ordinary matter.
We might expect equal proportion of mirror and ordinary matter. However with the A-A' axial force broken, we will have two species of heavy neutrinos, mirror plus ordinary, and mirror minus ordinary with some mass difference between the two. The heavy state would then decay to the lighter version, leaving an differing total of mirror and ordinary states, depending on the decay rates and branching ratios to matter and anti-matter.
It would seem that the axial force and mirror-matter theory, work well together aiding each other
to produce an nearly complete theory of the universe, together explaining both dark matter, dark energy, the breaking of parity, and predominance of matter over anti-matter.
Finally It is possible that mirror matter may be directly detected soon, in Higgs experiments. Robert Foot et al, have speculated that recent signs of a Higgs boson at the Tevetron but with half its expected cross section, may be due to Higgs mirror Higgs mixing, leaving a summed state around 140GeV, and a differenced state around 120GeV. Both states would have half the usual cross section and decay half the time in detectable particles, and half the time into mirror matter which would show up in the cross sections.