Dark matter is the mysterious stuff that cosmologists believe fills our Universe. The evidence for its existence is that there is not enough visible mass to hold galaxies together. But since galaxies manifestly do not fly apart, there must be some invisible stuff, some missing mass, that generates the gravitational forces holding them together.

But there’s a problem with this idea. Two of them actually. First, physicists’ best guess at the laws of physics give a good description of all of the particles they’ve discovered so far and a few they expect to discover soon. The trouble is that none of these particles have the right kind of properties to be dark matter ie electrically neutral, long-lived and slow moving. But none of the known or reasonably hypothesised particles fits the bill. To make room for a dark matter particle, the laws of physics have to be changed in ways that many theorists feel uncomfortable with.

Second, despite a decade spent searching for dark matter with experiments costing tens of millions of dollars, nobody has laid eyes on the stuff. Most physicists think these experiments have found nothing: zip, zilch, zero.

It’s hard to escape the conclusion that some other explanation for the missing mass is needed.

Enter Paul Frampton at the University of North Carolina and a few buddies. Frampton’s suggestion is that the missing mass is made up of black holes that are too small to see directly but too big to have evaporated away due to Hawking radiation.

But this idea is more than another wild guess. Frampton and pals have an interesting argument based on entropy to back up their claim. It goes like this.

First they determine what the maximum entropy of the Universe could be by imaging that the entire visible universe were a giant black hole. The answer turns out to be 10^123, a very big number. So that’s the upper limit on what the entropy can be.

Next, they work out a lower limit by adding together the entropy in all the known black holes in the universe. They work this out by assuming that there’s a giant black hole at the centre of every galaxy, a view that is increasingly commonly held by astrophysicists.

That gives the number 10^103, many orders of magnitude lower.

This a great deal of entropy, to be sure, but Frampton and co so it is unlikely to be the major contributor in our universe. “Each supermassive black hole is about the size of our solar system or smaller and it is intuitively unlikely that essentially all of the entropy is so concentrated,” he says. So something else must be generating entropy somewhere.

It can’t be visible matter since conventional calculations indicate that its entropy adds up to only 10^88. What’s left is the entropy of the missing dark mass.

What type of black holes could be responsible for this? It turns out that any black hole bigger than 10^6 solar masses would cause nearby matter to spiral into it, preventing galaxies from forming. Anything smaller than 10^-8 solar masses would have evaporated.

So the conclusion is that dark matter is made up of black holes with a mass of between 10^6 and 10^-8 solar masses.

But there’s a problem with this idea too. How could these black holes have formed in such large numbers early in the Universe. Something must have caused matter to clump together at this scale to form the black holes. But there is nothing to indicate how this might have happened in the present theory of inflation, which describes how the early Universe grew.

hat’s easily solved say Frampton and co: there must have been two periods of inflation. The first led to the large scale structure of the Universe that we see and has been measured by spacecraft such as WMAP. The second led t the clumping that created large numbers of medium-sized primordial black holes.

That’s an explanation that is a little easier to stomach than one in which the laws of physics must change to create new dark matter particles. But only just.

However Frampton’s ideas can be better tested by looking for evidence of these primordial black holes, which should cause microlensing events: ie their gravity should focus the light from stars behind them as seen from Earth.

Those kinds of measurements are getting easier to do so it should be possible to acept or reject Frampton’s ideas in the not too distant future.

Refs:

arxiv.org/abs/1003.3356: Black Holes Constitute All Dark Matter

arxiv.org/abs/1001.2308: Primordial Black Holes As All Dark Matter