The theoretical density that would create a flat Universe is called the critical density. We do not know the critical density exactly because we do not know Hubble's value accurately. The critical density is aroundor the equivalent of thirty proton masses every cubic metre, which might sound very small given thatof water contains aboutmolecules orproton masses, but the Universe is mostly empty space, with vast voids of nothingness.
The density of the Universe is very hard to determine experimentally. We can estimate the mass of a galaxy by counting the stars for example, but this gives a mass that is maybe one hundred times to small. Even allowing for gas and non visible matter such as neutron stars, black holes, brown dwarfs still gives a density much smaller than we believe to be the case from observing the motions of galaxies. We believe there must be about ten times more matter than can be accounted for by all the ordinary matter in the Universe – if you can say that black holes and neutron stars are made up of ordinary matter.
To resolve the paradox, scientists have hypothesised a form of matter called 'dark matter'. We think the dark matter must be there because we need it to explain the motions of galaxies, but we cannot see it or detect it – it does not radiate energy or radiation.
We know very little of the nature of dark matter. Whatever it is, it must constitute about 90% of the mass of the Universe. There are various theories as to what dark matter might be:
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Galaxies may contain a lot of mass in the form of failed stars or black holes. These it is said, might surround galaxies in a halo, so they are given the collective name Massive Astronomical Compact Halo Objects or MACHOs.
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Neutrinos. These exist in huge numbers – there are believed to be many more than any other type of particle. We do not know if the neutrino has a mass but if it does, be it ever so tiny, there are so many neutrinos that they could account for the missing mass.
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Hypothesised heavy particles that interact very weakly with matter so are very hard to detect. These are collectively called Weakly Interacting Heavy Particles of Wimps.
We may not fully understand the nature of space. We know in fact that Einstein's General Theory of Relativity is incomplete because it breaks down at the singularity inside a black hole. There exist some very exotic theories – supersymmetry and string theory – which have still to be fully developed but which may offer a way out of the paradox of the missing matter in a way we cannot yet imagine.