QUANTUM SCALAR FIELD IN THE FRW UNIVERSE WITH A CONSTANT ELECTROMAGNETIC BACKGROUND

We discuss a massive scalar field with conformal coupling in the Fried mann-Robertson-Walker (FRW) Universe of a special type with a constant electromagnetic field. Treating an external gravitational-electromagn etic background exactly, at the first time the proper-time representat ions for out-in, in-in and out-out scalar Green functions are explicit ly constructed as proper-time integrals over the corresponding (comple x) contours. The vacuum-to-vacuum transition amplitudes and the number of created particles are found and vacuum instability is discussed. T he mean values of the current and the energy-momentum tensor are evalu ated, and different approximations for them are investigated. The back reaction of the particles created to the electromagnetic field is est imated in different regimes. The connection between the proper-time me thod and the effective action is outlined. The effective action in sca lar QED in the weakly curved FRW Universe (de Sitter space) with a wea k constant electromagnetic held is found as a derivative expansion ove r curvature and electromagnetic field strength. Possible further appli cations of the results are mentioned.