Refined Swampland conjecture in deformed Starobinsky gravity

In order to validate or invalidate a large class of low energy effective theories, the Swampland conjecture has attracted significant attention, recently. It can be stated as inequalities on the potential of a scalar field which is conjectured to satisfy certain constraints. In this work, we discuss the theoretical viability of deformed Starobinky gravity in light of the refined Swampland conjectures. We consider the deformation of the form $f(R)\sim R^{2(1-\alpha)}$ with $\alpha$ being a constant. We then constrain $\alpha$ using the spectral index of curvature perturbation $n_s$ and the tensor-to-scalar ratio $r$. We demonstrate that the model under consideration is in strong tension with the refined swampland conjecture. However, regarding our analysis with proper choices of parameters $a,\,b=1- a$ and $q$, we discover that the model can always satisfy this new refined swampland conjecture. Therefore, the model might be in landscape since the further refining de Sitter swampland conjecture is satisfied.