Curvature corrections to Starobinsky inflation can explain the ACT results (2505.10305v2)

Abstract: We investigate the impact of curvature corrections to Starobinsky inflation in light of the latest observational results from the Atacama Cosmology Telescope (ACT). While the pure Starobinsky model remains a compelling candidate for cosmic inflation, we explore how the higher-order curvature terms $R^3$, $R^{4}$ and $R^{3/2}$ modify the inflationary predictions. Using the scalar-tensor formulation of $f(R)$ gravity, we derive the effective scalar potentials and compute the resulting scalar tilt $n_s$, its running index $\alpha_s$ and the tensor-to-scalar ratio $r$. We show that those curvature corrections can shift the predictions to align better with the ACT data, thus providing a possible resolution to a minor discrepancy between the standard Starobinsky model and ACT observations. Our findings suggest that the modified Starobinsky models with the higher-order curvature terms offer a viable pathway to reconciling inflationary predictions with precision cosmological measurements. At the same time, measuring or constraining primordial tensor modes can help to discriminate between these corrections.