= Solution
The supplied <slow-roll curvature power spectrum> simplifies to
$$
\mathcal P_{\mathcal R}=\frac{V}{24\pi^2M_{\rm Pl}^4\epsilon_V}.
$$
At a fixed <number of e-folds> before the end, multiplying the potential by a constant does not change $V'/V$, $V''/V$ or the slow-roll field value. It multiplies $\mathcal P_{\mathcal R}$ by that constant. Thus, for an unchanged subsequent cosmology,
$$
\boxed{V_0\mapsto2V_0:\qquad P_m(k,0)\mapsto2P_m(k,0).}
$$
The <scalar spectral index>, transfer-function shape, turnover and acoustic features are unchanged at this order. Root-mean-square density fluctuations increase by $\sqrt2$. The comparison uses the same exit e-fold count; a different specified reheating history could shift the detailed mapping between $k$ and that count.
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