Sub-Planckian $\phi^{2}$ Inflation in the Palatini Formulation of Gravity with an $R^2$ term

Understand

In the context of the Palatini formalism of gravity with an $R^{2}$ term, a $\phi^{2}$ potential can be consistent with the observed bound on $r$ whilst retaining the successful prediction for $n_{s}$.

• Here we show that the Palatini $\phi^{2} R^2$ inflation model can also solve the super-Planckian inflaton problem of $\phi^{2}$ chaotic inflation, and that the model can be consistent with Planck scale-suppressed potential corrections.
• If $\alpha \gtrsim 10^{12}$, where $\alpha$ is the coefficient of the $R^2$ term, the inflaton in the Einstein frame, $\sigma$, remains sub-Planckian throughout inflation.
• In addition, if $\alpha \gtrsim 10^{20}$ then the predictions of the model are unaffected by Planck-suppressed potential corrections in the case where there is a broken shift symmetry, and if $\alpha \gtrsim 10^{32}$ then the predictions are unaffected by Planck-suppressed potential corrections in general.