Challenges for Large-Field Inflation and Moduli Stabilization

We analyze the interplay between K"ahler moduli stabilization and chaotic inflation in supergravity. While heavy moduli decouple from inflation in the supersymmetric limit, supersymmetry breaking generically introduces non-decoupling effects. These lead to inflation driven by a soft mass term, $m_{\phi }^2\sim m{m}_{3\mathrm{/}2}$, where $m$ is a supersymmetric mass parameter. This scenario needs no stabilizer field, but the stability of moduli during inflation imposes a large supersymmetry breaking scale, $m_{3\mathrm{/}2}\gg H$, and a careful choice of initial conditions. This is illustrated in three prominent examples of moduli stabilization: KKLT stabilization, K"ahler Uplifting, and the Large Volume Scenario. Remarkably, all models have a universal effective inflaton potential which is flattened compared to quadratic inflation. Hence, they share universal predictions for the CMB observables, in particular a lower bound on the tensor-to-scalar ratio, $r\gtrsim 0.05$.