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How Critical Density Was Calculated.

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Posted by Alexander on July 2, 2001 23:53:39 UTC

If you take a large cube containing many receeding galaxies (and other matter) with the total mass m, and calculate their: rest mass energy (mc^2) plus kinetic energy (from known Hubble constant) plus gravitational potential energy of interaction of galaxies, you will obtain some number which can be positive or negative depending on how much mass m you have per volume of this cube (i.e., on the average density of matter in the cube). It turns out, that at certain density (called critical - about 8x10^-27 kg.m^3) total energy will be zero. This density corresponds to the border between closed (neg curvature) and open (pos. curvature) universe.

While visible matter in universe has density barely 10% of critical, gravitational field felt by galaxies is stronger than the field created by this visible mass alone as much as several times, suggesting that there is at least 3-4 times more of unseen "dark matter" around. Even Sun feels presence of that matter: it orbits Milky Way twice faster than would be without it.

Some resent measurements (details of which I do not know) also suggest that overall universe is likely flat, which means that average density dencity is critical or very close to critical).

What constitutes "dark matter" - ordinary objects like brown dwarfs, black and neutron stars or some WIMPs (weakly interacting massive particles) like neutrino or others is still open question, but there are more and more facts in favor of average density of universe being close to critical density.

Another strong support to the critical density comes from inflation: deviations from critical density greatly amplify during inflationary phase of "big bang", making overcritical universe wuickly stop expansion and collapse back due to excess of gravitational energy, and making undercritical universe expand with such ever groving acceleration that it would almost completely empty (density many orders less than critical)and very quickly.

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