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 relativistic barotropic fluid interpretation) are studied. The eigenvalues of the tangent map for the resulting Hamiltonian system are used to classify the phase space regions and to understand the typical toy-universe evolution. After a transient, inflation is obtained in the hyperbolic (real eigenvalues) region. This new independent eigenvalue-based inflationary criterion is shown to be compatible and complementary to the standard slow roll-over conditions. For the later evolution of the toy-universe, a family of adiabatic trajectories oscillating about a conventional cosmology filled with a relativistic fluid is obtained once the system falls into the elliptic (imaginary eigenvalue) regions. The corresponding thermodynamic functions are computed.