Dynamical properties of the conformally coupled flat FRW model - art. no. 107302

In this paper we study the dynamical behavior of a simple cosmological mode l defined by a spatially Rat Robertson-Walker geometry, conformally coupled with a massive scalar held. We determine a Lyapunov-like function for the nonlinear evolution equations. From this function we prove that all the sta tionary solutions are unstable. We also show that all initial conditions, d ifferent from the stationary points, originate an expanding universe in the asymptotic regime, with a scale parameter a(t) that goes to infinity and t he scalar field phi(t) that goes to zero in an oscillatory way. We also fin d two asymptotic solutions, valid for sufficiently large values of time. Th ese solutions correspond to a radiation dominated phase and to a matter dom inated phase, respectively.