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Another motivation for studying whether neutrinos have mass or not is to try and determine whether neutrinos form part of the famous dark matter problem. Astrophysicists have been observing for some time that the rotational speed of galaxies is not what they would expect if the total mass of the visible stars made up the total mass of the galaxy. The rotational velocity of the stars at the edges of galaxies is much larger than what would be expected if most of the mass of the galaxy was concentrated close to its centre (galactic rotational curves). This implies that there must be an "invisible" form of mass that goes out to the edges of galaxies forming a halo of dark matter. Calculations of the percentage of dark matter vary, but it is believed that the visible matter makes up only between 1% and 10% of the total mass of the universe. The amount of dark matter is a crucial parameter to know if we want to determine what is the future fate of the universe. If the mass of the universe is above a certain critical mass, the current expansion would eventually halt and the universe would commence an implosion into itself, resulting in a "big crunch" at some time in the distant future. If the universe is below this critical mass, then the universe would continue to expand for ever and if it was at exactly the critical mass then it would also continue to expand but at a continuously slower rate.
There are a number of candidates for this dark matter: some are astronomical objects like MACHOs (Massive Astronomical Compact Halo Objects) which are low mass stars like brown dwarves or large planets similar to Jupiter or black holes with masses of less than a solar mass, or sub-atomic particles that have yet to be discovered (like Weakly Interacting Massive Particles or WIMPS, and axions) or neutrinos with a mass of the order of 1-30 eV. It is worth noting that MACHOs have already been discovered by the MACHO and EROS collaborations by the technique of gravitational lensing, in which the image of a distant object is amplified by a massive object in the light path between the earth and the far-away object, but the number of these objects is not sufficient to explain the whole dark matter story. There are many other experiments that are searching for dark matter and links to these experiments can be found through the UK dark matter search site .
It is well known that there is a cosmic microwave background that permeates the universe with an average temperature of 2.726 K. The observed universe shows rather clumpy features (large voids and areas of the universe with clusters of galaxies) and the uniformity of the microwave background in the universe seemed at odds with this clumpy structure. The Cosmic Observatory Background Explorer satellite (COBE) was launched to search for ripples in the microwave background that would be compatible with the clumpiness of the observed universe. The discovery of these ripples was made in 1992, in which it was found that the temperature of the microwave background varied by differences of about one thousandth of a degree in different parts of the sky. This was a triumph for the Big Bang theory of the universe, since it verified that the origin of the microwave background was in effect the remnant radiation from that Big Bang after cooling for more than 10 billion years and that these ripples formed the density fluctuations needed to form the large scale structure of the universe. Models that explain these fluctuations include the dark matter, and the COBE data favours a model in which there is a 70% cold dark matter (objects like MACHOS, WIMPS and axions which travel at non-relativistic speeds) and a 30% hot dark matter (like neutrinos which are relativistic particles) component. This still leaves the possibility open that neutrinos could make up about 30% of the dark matter. A logical candidate could be the tau-neutrino which could possibly be the heaviest of the neutrinos (assuming a mass-heierchy amongst neutrinos). This is one of the main motivations in the search for muon to tau-neutrino oscillations at experiments like NOMAD and CHORUS.