Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 9D / c / Solution

During inflation $w\simeq -1$, so $1+3w\simeq -2$. For expansion,and the arrows point toward $\Omega =1$. Equivalently, accelerated expansion makes the curvature contribution $|k{c}^2|/{\mathcal{H}}^2$ rapidly decay. A sufficiently long inflationary epoch therefore drives a broad range of initial conditions extremely close to spatial flatness.