The recollapse problem of closed Friedmann-Robertson-Walker models in higher-order gravity theories

We study the closed universe recollapse conjecture for positively curved Friedmann-Robertson-Walker models with a perfect fluid matter source and a scalar field which arises in the conformal frame of the R+alpha R-2 theory. By including ordinary matter, we extend the analysis of a previous work. We analyze the structure of the resulted four-dimensional dynamical system with the methods of the center manifold theory and the normal form theory. It is shown that an initially expanding closed FRW universe, starting close to the Minkowski space-time, cannot avoid recollapse. We discuss the possibility that potentials with a positive minimum may prevent the recollapse of closed universes. (c) 2005 American Institute of Physics.