Divergences in a nonsteady universe

The structure of divergences of the vacuum mean energy-momentum tensor is investigated by a simple model (a linear massive scalar field with nonconformal coupling in a spatially plane isotropic universe). The class R of physically permissible vacuums [0> is isolated; when∥0>?R the tensor contains only standard local (power-law and logarithmic) divergences; in the general case the condition that the Hamiltonian be diagonal and the “quantum equivalence principle” lead to ∥0>?R . The nongeometric structure of power-law divergences, which does not allow their elimination by renormalization of the constants in the generalized gravitational action, is established by a new regularization method (covariant smoothing of a δ-function). It is shown that all local divergences are eliminated by renormalization according to the Pauli-Villars scheme; it gives the same final results as do the adiabatic and n-wave computational procedures.