Quantum fields in Bianchi type I spacetimes. The Kasner metrc

Vacuum polarization of the quantized massive fields in Bianchi type I spacetime is investigated from the point of view of the adiabatic approximation and the Schwinger-DeWitt method. It is shown that both approaches give the same results that can be used in construction of the trace of the stress-energy tensor of the conformally coupled fields. The stress-energy tensor is calculated in the Bianchi type I spacetime and the back reaction of the quantized fields upon the Kasner geometry is studied. A special emphasis is put on the problem of isotropization, studied with the aid of the directional Hubble parameters. Similarities with the quantum corrected interior of the Schwarzschild black hole is briefly discussed.