Frame-Dependence of the Hamilton-Jacobi Formalism for Inflation and Reheating in Non-Minimal Gravity
arXiv:2502.16262 · doi:10.1140/epjc/s10052-025-14968-3
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.
21 pages, 16 figures, 2 tables
References in corpus (24)
- The Standard Model Higgs boson as the inflaton
- BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season
- Nonperturbative Dynamics Of Reheating After Inflation: A Review
- Primordial Black Holes and Slow-Roll Violation
- Reheating constraints to inflationary models
- Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
- Reheating predictions in single field inflation
- Higgs inflation with loop corrections in the Palatini formulation
- Reheating in Palatini inflationary models
- Resurrecting Quadratic Inflation with a non-minimal coupling to gravity
- Inflationary Perturbations in Palatini Generalised Gravity
- Probing reheating with primordial spectrum
- Curing inflationary degeneracies using reheating predictions and relic gravitational waves
- Inflationary dynamics and preheating of the non-minimally coupled inflaton field in the metric and Palatini formalisms
- Hamilton-Jacobi formalism to warm inflationary scenario
- Constraining the general reheating phase in the -attractor inflationary cosmology
- Hamilton-Jacobi Formalism for Tachyon Inflation
- Probing the reheating phase through primordial magnetic field and CMB
- Growth of power spectrum due to decrease of sound speed during inflation
- Primordial non-Guassianity in inflation with gravitationally enhanced friction
- Separatrices in the Hamilton-Jacobi Formalism of Inflaton Models
- A Jacobian elliptic single-field inflation
- Kinetic dominance and psi series in the Hamilton-Jacobi formulation of inflaton models
- Hamilton-Jacobi formalism for k-inflation