COBE normalization of quartic hilltop inflation ($\alpha ={\pi }^2{\mathcal{P}}_{\mathcal{R}}/(8N^3)$)

For a negligible tensor contribution, the historical COBE horizon amplitude ${\delta }_H\sim 2\times 10^{-5}$ corresponds to curvature power ${\mathcal{P}}_{\mathcal{R}}\sim 25{\delta }_H^2/4$. In quartic hilltop inflation, $\alpha ={\pi }^2{\mathcal{P}}_{\mathcal{R}}/(8N^3)$ is of order $10^{-14}$ at $N=50$, independent of the small symmetry-breaking scale at this order. The exact inferred amplitude depends on the late cosmology and tilt used in the COBE transfer calculation.

// Target: cosmic-inflation.bigb