Spontaneous breaking of $CP$-symmetry in a nonstationary isotropic metric

It is shown that when a massless scalar field and a massive fermion field interact in a spacetime with homogeneous isotropic metric of open type an effect of spontaneous breaking of $P$ and $CP$ symmetry arises. The method of diagonalization of the Hamiltonian by Bogolyubov transformations is used to obtain expressions for the number density of the produced pairs, the density of the chiral charge, and the pseudoscalar density of fermions. The correction to the number density of produced particles resulting from the effect of the spontaneous symmetry breaking is calculated.