Loss of coherence in multidimensional minisuperspaces

In the semiclassical limit of quantum gravity, solutions to the Wheeler-DeWitt equation involve several WKB components. In order to reach the adequate classical limit these contributions should not interfere. We show here that this is in general the case. We work with a general minisuper-space model with perturbations and we construct the reduced density matrix $\tilde{\rho }(g_A, g_A^{\prime })$ by tracing out all the nonrelevant modes of the environment. It turns out that not only are the off-diagonal terms of $\tilde{\rho }(g_A, g_A^{\prime })$ strongly suppressed but the quantum contributions to $\tilde{\rho }(g_A, g_A)$ due to interference between different semiclassical solutions also vanish. As an example we discuss the particular case of the Kantowski-Sachs cosmological model.