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,
$m_\varphi^2 \sim m m_{3/2}$, 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, $m_{3/2} \gg H$, 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, $r \gtrsim 0.05$.
