Very Cold Dark Matter

To a first approximation, what the Lambda Cold Dark Matter (LCDM) model of cosmology gets right is the Cosmic Microwave Background radiation (CMB). In other words, it gets the overall scale of the universe right. The smaller things get, the more difficulty it has. At galaxy scales it has great difficulty producing a type of dark matter that interacts with ordinary matter in just the right way to produce the detailed properties that are observed. At wide binary scales (of the order of a light-week) LCDM is apparently ruled out entirely.

But this depends on the properties of the “dark matter”. Given that essentially all possibilities have been ruled out, we must look again at the arguments, and see if there is a hidden (and possibly false) assumption in any of them. In the previous post, I identified one such hidden assumption, which is that the half-life of a free neutron is a universal constant. This is not just a hidden assumption, it is one that appears to be false, according to experiments conducted on Earth. Today, the discrepancy amounts to 3 sigma, that is to say, a confidence level of 99.7%. This is pretty good, but not good enough for physicists to say they are really confident (for that, they insist on 5 sigma, or about 99.9999%).

Anyway, experiment strongly suggests that the half-life of a free neutron is not a universal constant. And if it is not a constant, what does it depend on? In the usual theory, it depends on the amount of free energy there is available to drive the decay, that is, on the relative mass difference between the neutron itself and the decay products. On the Earth, we measure this energy difference at about .08%, which is a very small amount of energy, so the half-life is very long. But if the half-life depends on the environment, as experiment suggests, then in particular it may depend on things like the rotation of the Earth.

That is where my empirical formulae for the electron/proton/neutron mass ratios come in, that suggest a dependence on the number of days in a year, and on the angle of tilt of the Earth’s axis. The number of days in a year is constant enough that it won’t affect experimental results, but the angle of tilt is not. As the angle of tilt decreases, the amount of free energy increases very slightly, so the half-life decreases. but the angle of tilt varies in quite a complicated way, sometimes increasing, sometimes decreasing, in a predictable pattern including an oscillation with a period of 18.6 years. In particular, this variation is complicated enough that the pattern will not be obvious just by looking at the experimental data. But the inconsistency of the results may be obvious.

In fact, the inconsistency is at present attributed to a difference between the types of experiments that are used to make the measurement. This is a possibility, of course, but I think it is more likely to be independent of the type of experiment, and dependent on the timing of the experiment. Anyway, all this is highly speculative, and all we can really say is that the assumption of a universal constant half-life of a free neutron is an unsafe assumption. Even on Earth, it seems unsafe, let alone in the wider universe.

So we need a new assumption about the half-life of a free neutron, that is compatible with observations of the cosmos. We need an assumption that free neutrons are stable on scales of the lifetime of the universe, provided they are far enough away from any stars or galaxies or any other larger concentrations of matter. How far away is far enough? MOND phenomenology suggests that we measure this in terms of the strength of the gravitational field, that is the acceleration due to gravity, and that the critical acceleration is roughly the same as the acceleration of the Solar System towards the centre of the Milky Way.

With this assumption, free neutrons that are closer to the centre of the Milky Way will eventually decay, and the decay products will eventually be captured by the magnetic fields of stars, and on the timescale of the age of the galaxy, there will be nothing left of them. But free neutrons that are more than about 1.5 times as far away from the centre as we are will never decay at all, and however many there were to begin with, they are still there, forming a halo of baryonic dark matter, that is so cold that it cannot be seen. That is why I call it Very Cold Dark Matter (VCDM).

VCDM has very different properties from the usual assumptions for CDM. Ordinary CDM should clump together in the centres of galaxies, but VCDM does not: as soon as it gets anywhere near the galactic centre, it decays, and vanishes in a puff of smoke. We can’t see it, because it isn’t there. We can’t detect it as we pass “through” it, because it isn’t there. The Solar System has cleared it all out of the way billions of years ago. It isn’t there. But it is out there on the edges of the galaxy, where no-one can see it.

Now, how much VCDM do you think there is? Well, analysis of the CMB indicates that it should comprise about 85% of the matter in the universe. In other words, matter is about 85% neutrons, 14% hydrogen, and 1% everything else. Not unreasonable, I think. Most of the neutrons are in the regions of space that are far away from any stars or galaxies, and we know that the universe is full of such enormous “voids”. But perhaps they are not as empty as we think.

So far so good, but here is the acid test: can free neutrons explain the behaviour of wide binaries in our neck of the woods? First we have to look at where the VCDM is in the galaxy. I have suggested a sharp cutoff point about 1.5 times larger than our orbit in the galaxy, but this is likely to be an over-simplification. It could fall off quite gradually, if the half life of the neutron becomes very long, but not quite infinite. So let’s suppose that there is some VCDM surrounding a wide binary. What happens to it? Within the system, much of it falls into one star or the other, decays and disappears. But not all of it. VCDM sitting in the middle will continue just sitting there, increasing the effective mass of each star as seen by the gravitational attraction on the other.

What does this look like phenomenologically? It looks like increasing the active gravitational mass of each star, while having no effect on the inertial mass. It looks like a modified gravity (MG) version of MOND. What does observation say? It depends who you believe, but I would say that phenomenologically, wide binaries look like MOND, and not like LCDM. And I would also say that VCDM also looks like MOND, and therefore looks like observations.

So there you have it, my model of cosmology in a nutshell, the VCDM model. Perhaps you also want me to address the question of Dark Energy (Lambda)? Well, let me have another sleepless night to think about that, and I’ll tell you my conclusions tomorrow.