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Stress-Energy Tensor of the Quantized Massive Fields in Friedman-Robertson-Walker Spacetimes

The approximate stress-energy tensor of the quantized massive scalar, spinor and vector fields in the spatially flat Friedman-Robertson-Walker universe is constructed. It is shown that for the scalar fields with arbitrary curvature coupling, $ξ,$ the stress-energy tensor calculated within the framework of the Schwinger-DeWitt approach is identical to the analogous tensor constructed in the adiabatic vacuum. Similarly, the Schwinger-DeWitt stress-energy tensor for the fields of spin 1/2 and 1 coincides with the analogous result calculated by the Zeldovich-Starobinsky method. The stress-energy tensor thus obtained are subsequently used in the back reaction problem. It is shown that for pure semiclassical Einstein field equations with the vanishing cosmological constant and the source term consisting exclusively of its quantum part there are no self-consistent exponential solutions driven by the spinor and vector fields. A similar situation takes place for the scalar field if the coupling constant belongs to the interval $ξ\gtrsim 0.1.$ For a positive cosmological constant the expansion slows down for all considered types of massive fields except for minimally coupled scalar field. The perturbative approach to the problem is briefly discussed and possible generalizations of the stress-energy tensor are indicated.