Global dynamics of cosmological expansion with a minimally coupled scalar field

We give a complete description of the asymptotic behavior of a Friedmann-Robertson-Walker Universe with 'normal' matter and a minimally coupled scalar field. We classify the conditions under which the Universe is or is not accelerating. In particular, we show that only two types of large time behavior exist: an exponential regime, and a subexponential expansion with the logarithmic derivative of the scale factor tending to zero. In the case of the subexponetial expansion the Universe accelerates when the scalar field energy density is dominant and the potential behaves in a specified manner, or if matter violates the strong energy condition rho + 3 p > 0. When the expansion is exponential the Universe accelerates, and the scaler field energy density is dominant. We find that for the Big Bang to occur at zero scale factor, the equation of state of matter needs to satisfy certain restrictions at large densities. Similarly, a never ending expansion of the Universe constrains the equation of state at small matter densities. (C) 2000 Elsevier Science B.V. All rights reserved.