Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 53 / 4 / 2 / Solution

The supplied slow-roll curvature power spectrum simplifies toAt a fixed number of e-folds before the end, multiplying the potential by a constant does not change $V^{\prime }/V$, $V^{\prime \prime }/V$ or the slow-roll field value. It multiplies ${\mathcal{P}}_{\mathcal{R}}$ by that constant. Thus, for an unchanged subsequent cosmology,The scalar spectral index, transfer-function shape, turnover and acoustic features are unchanged at this order. Root-mean-square density fluctuations increase by $\sqrt{2}$. The comparison uses the same exit e-fold count; a different specified reheating history could shift the detailed mapping between $k$ and that count.