Inflation within closed friedmann universe models

Abstract

For the LagrangianL = R ²,the de Sitter space-time is known to be an attractor solution. Here, we classify for closed Friedmann models in which initial conditions lead asymptotically to a de Sitter phase and what the behaviour is for the other solutions. Four types of solutions form together a generic set, and three of them are asymptotically de Sitter; the fourth one has both an initial and final singularity. Furthermore, exactly seven other solutions exist and can be given in closed form. Three of them are known, the other four are new and have a linear asymptotic behaviour of the cosmic scale factor.