@Laurelai The current UN demographic view (mid fertility model) is no peak this century. Global population seems to be following a logistic curve and at the moment we're in the middle of the linear, middle part of the curve.

However that simple S-Curve is too simplistic (IMHO). It's a mathematical abstraction, extrapolation model with not enough variables. For instance, you can't predict population without also predicting energy availability and pollution effects.