Stability of Gaussian approximations in minisuperspace: A variational approach

Stability results are obtained for some special cases of finite-dimensional approximations in minisuperspace field theory, using both rigorous methods, based on theorems of the Kolmogorov-Arnold-Moser type, as well as perturbation theory. For a $\lambda {\phi }^4$ theory and a lower-dimensional truncation of the Hamiltonian, it is shown that the evolution of coherent states in the homogeneous minisuperspace sector is indeed stable for positive values of the parameters that define the field theory. It is also shown that for more realistic field-theoretical models, however, Arnold diffusion could have destabilizing effects over very long times. The relevance of such a phenomenon requires consideration of each case separately.