Clearing the Brush: The Last Stand of Solo Small Field Inflation

Abstract

By incorporating both the tensor-to-scalar ratio and the measured value of the spectral index, we set a bound on solo small field inflation of $\Delta \varphi /m_{Pl}\ge 1.00\sqrt{r/0.1}$. Unlike previous bounds which require monotonic ${\epsilon }_V,$ $|{\eta }_V|<1$, and 60 e-folds of inflation, the bound remains valid for non-monotonic ${\epsilon }_V$, $|{\eta }_V|\gtrsim 1$, and for inflation which occurs only over the 8 e-folds which have been observed on the cosmic microwave background. The negative value of the spectral index over the observed 8 e-folds is what makes the bound strong; we illustrate this by surveying single field models and finding that for $r\gtrsim 0.1$ and 8 e-folds of inflation, there is no simple potential which reproduces observed CMB perturbations and remains sub-Planckian. Models that are sub-Planckian after 8 e-folds must be patched together with a second epoch of inflation that fills out the remaining $\sim 50$ e-folds. This second, post-CMB epoch is characterized by extremely small ${\epsilon }_V$ and therefore an increasing scalar power spectrum. Using the fact that large power can overabundantly produce primordial black holes, we bound the maximum energy level of the second phase of inflation.

arXiv comment12 pages, 5 figures, references added, published in PRD

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