https://doi.org/10.1140/epjc/s10052-025-13787-w
Regular Article - Theoretical Physics
Hamilton–Jacobi method in non-minimal coupling inflation: metric vs. Palatini
1
School of Nuclear Science and Technology, University of South China, 421001, Hengyang, China
2
School of Mathematics and Physics, University of South China, 421001, Hengyang, China
3
Hunan Key Laboratory of Mathematical Modeling and Scientific Computing, University of South China, 421001, Hengyang, China
Received:
26
September
2024
Accepted:
4
January
2025
Published online:
23
January
2025
The Hamilton–Jacobi approach offers a natural framework for analyzing inflationary dynamics, relying on the specified Hubble parameter rather than the potential, particularly in extended gravity theories. In this study, we apply this method to investigate inflation with non-minimal coupling, comparing the metric and Palatini formulations. Using a power-law Hubble parameter in the Jordan frame, we find that both formalisms satisfy the attractor condition, with a slight suppression in the Palatini case. Our results align closely with the latest observational data, demonstrating the Palatini formalism’s heightened sensitivity to coupling constants and model parameters. Furthermore, we show that within the model’s viable parameter space, the reheating process can achieve sufficiently high temperatures to support successful leptogenesis.
© The Author(s) 2025
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