= Inflaton clock-shift origin of curvature perturbations
{title2=$\mathcal R=H\delta\phi_{\rm flat}/\dot\phi$}
On a single-field attractor, a field fluctuation changes the local point along the background trajectory. The corresponding time shift has magnitude $|\delta\phi/\dot\phi|$, and local expansion converts it into curvature of magnitude $H|\delta\phi/\dot\phi|$. On spatially flat slices a standard sign convention gives $\mathcal R=H\delta\phi_{\rm flat}/\dot\phi$. The vacuum mode amplitude $H/(2\pi)$ then determines the scalar curvature spectrum.
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