Calculation of the energy-momentum tensor of the vacuum in an anisotropic universe

Subtractive methods (N-wave and adiabatic) which are applicable to the calculation of the energy-momentum tensor of quantum fields in curved space-time are in need of a foundation in terms of renormalizations. In the example of a scalar field in an anisotropic universe of Bianchi type I it is shown that the Pauli-Villars scheme, in which the renormalization is in fact realized separately in each mode, provides such a foundation. The technical difficulty obstructing the explicit regularization of divergent integrals in momentum space is shown. We calculate the polarization of the vacuum of a scalar field with arbitrary coupling to the curvature in a weakly anisotropic universe