Generic inflationary and noninflationary behavior in toy-cosmology

Cosmological solutions of a toy homogeneous isotropic universe filled with a superfluid Bose condensate described by a complex scalar field (with rela tivistic barotropic fluid interpretation) are studied. The eigenvalues of t he tangent map for the resulting Hamiltonian system are used to classify th e phase space regions and to understand the typical toy-universe evolution. After a transient, inflation is obtained in the hyperbolic (real eigenvalu es) region. This new independent eigenvalue-based inflationary criterion is shown to be compatible and complementary to the standard slow roll-over co nditions. For the later evolution of the toy-universe, a family of adiabati c trajectories oscillating about a conventional cosmology filled with a rel ativistic fluid is obtained once the system falls into the elliptic (imagin ary eigenvalue) regions. The corresponding thermodynamic functions are comp uted. (C) 2000 Elsevier Science B.V. All rights reserved.