INVESTIGATION OF EARY UNIVERSE BASED ON UNIFIED THEORIES

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In most previous study of physical cosrnology effect of cosmic environment has been evaluated by using the Boltzmann equation suitably averaged in thermal medium. This approach is based on the on-shell S-matrix element, tire transition matrix element between the infinite past and the h6 : rite future, 'and neglects subtle quantum mechanical correlation at 6nite intermediate times of the on-going process. In the present investigation a fully quantum mechanical approach is adopted, using the in influence functional method. In particular, pair annihilation of heavy stable particle that occurs in the early universe was investigated, and quantum kinetic equation for the momentum distribution of the annihilating particle has been derived.A crossing symmetric Hartree approximation that determines self-consistently the equilibrium distribution is developed, and its Markovian approximation is shown to generalize the Boltzmann equation, including off-shell effects. The off-shell effect is dominant at low temperatures. The deck changes the equilibrium distribution from the familiar 1/(e^<omegamu/gamma>-1) modified one given by a Gibbs formula. Integrated over momenta, tire particle number density becomes roughly of order (coupling) * ROO<T/M>・T^3 at low 'temperatures for the S-wave annihilation. The relic mass density in the present universe is insensitive the coupling strength in a large range of the mass and the coupling parameters, and scales with the VAMP mass as <approximately equal> 6*10^4eVcm^<-3>(M/geV)^<4/3>