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Unformatted text preview: 35. The big bang and the evolution of the universe 35.1 The first minutes Let us suppose the universe is filled with non-relativistic matter and radiation (relativistic particles behave like radiation). What would be the effect of the expansion on the mass-energy densities? For non-relativistic matter the mass of the particles is conserved, as is the particle number. The frequency of the radiation is reduced, however. We can interpret that as a photon gas with energy = h , which then also decreases during the cosmological expansion. Therefore u m = m n m R- 3 non- relativistic matter (35 . 1) u r = n r R- 4 relativistic matter or radiation (35 . 2) At the present time the mass-energy density of ordinary matter is with m . 04 much larger than that of radiation. But on account of the different dependence on the scaling parameter the universe must have been essentially relativistic or radiation-dominated at earlier times. Then the Friedmann equation is no longer valid, for p = (1 / 3) u r 6 = 0. Very soon after the big bang the universe should have been exceedingly hot! One should note that the equation of state, p ( ), which is used to calculate the cosmological evolution, may not be known for the initial phase of the universal expansion. Laboratory experiments have allowed us to test the behaviour of matter up to energies around 100 GeV, corresponding to temperatures T 10 15 K. 35.2 The coupling between particles and radiation An important fact is that scattering processes between particles (and photons) should have been rather frequent in the early universe, and thus the energy distributions of all particles should have been thermal, that is Maxwell distributions or in the relativistic case Maxwell-Jutner...
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