Frame-dependence of the Hamilton–Jacobi formalism for inflation and reheating in non-minimal gravity

Abstract In this work, we investigate the Hamilton–Jacobi formalism for non-minimally coupled inflation, focusing on the methodological frame-dependence arising from its application in the Jordan and Einstein frames. We systematically compare the physical predictions from two distinct computational schemes: applying the Hamilton–Jacobi approximation before versus after the conformal transformation. This comparison is conducted for both the metric and Palatini formalisms. Our results, consistent with Planck data, reveal significant quantitative differences between the two schemes, highlighting a subtle frame-dependence in the approximation method. These discrepancies, observed in the spectral index, the tensor-to-scalar ratio, and reheating parameters, are more pronounced in the Palatini formalism. Our study emphasizes the sensitivity of cosmological predictions to the computational path chosen, and provides a quantitative analysis of this methodological uncertainty, offering valuable insights into the robustness of predictions in modified gravity.