Natural Inflation with non minimal coupling to gravity in $R^2$ gravity under the Palatini formalism

Understand

Natural Inflation with non-minimal coupling (NMC) to gravity, embodied by a Lagrangian term $\xi \phi^2 R $, is investigated in the context of an extended gravity of the form $R+ \alpha R^2$.

• The treatment is performed in the Palatini formalism.
• We discuss various limits of the model ``$\alpha \gg 1$'' and ``$\alpha \ll 1$'' in light of two scenarios of inflation: a ``Slow roll'' and a ``Constant roll'' scenario.
• By analyzing the observational consequences of the model, our results show a significant improvement regarding compatibility between the theoretical results of this model and the observational constraints from Planck 2018 and BICEP/Keck 2018, as exemplified by the tensor-to-scalar ratio and spectral index.