Intermediate inflation and the slow-roll approximation

It is shown that spatially homogeneous solutions of the Einstein equations coupled to a nonlinear scalar field and other matter exhibit accelerated expansion at late times for a wide variety of potentials $V$. These potentials are strictly positive but tend to zero at infinity. They satisfy restrictions on $V^{\mathrm{\prime }}\mathrm{/}V$ and $V^{\mathrm{\prime }\mathrm{\prime }}\mathrm{/}{V}^{\mathrm{\prime }}$ related to the slow-roll approximation. These results generalize Wald’s theorem for spacetimes with positive cosmological constant to those with accelerated expansion driven by potentials belonging to a large class.