Reheating-Imprinted Axion Initial Data as a Discriminant between Palatini and Metric Formulations
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This repository contains the source files for the manuscript
“Reheating-Imprinted Axion Initial Data as a Discriminant between Palatini and Metric Formulations.”
The work proposes a conservative discriminator between Palatini and metric formulations of gravity based on reheating-imprinted axion initial data. Assuming a common Einstein-frame derivative current portal, the analysis shows that formulation dependence can arise through differences in the post-inflationary reheating history, even when the portal itself is fixed.
An analytic scaling description is developed for the effective axion initial angle and its dependence on reheating parameters and endpoint quantities. The manuscript also discusses the Assumption A framework, the role of endpoint data, and possible extensions beyond the common-portal setup.
This upload contains the LaTeX source and related files for archival purposes.
v2:
This version corrects and sharpens the analytic scaling formula for the reheating imprint on axion initial data. In particular, the end-of-inflation matching factor is now treated consistently, so that the closed-form benchmark scaling depends on σend−1/2\sigma_{\rm end}^{-1/2}σend−1/2 rather than σend1/2\sigma_{\rm end}^{1/2}σend1/2. The corresponding expressions in the main text, abstract, discriminant formula, nuisance-factor discussion, and comparison table have been updated accordingly. The Jordan-to-Einstein frame appendix has also been cleaned up for consistency in the Palatini conformal map, and the endpoint derivation now explicitly states the assumption under which the residual decaying mode is neglected. In addition, the formulation-level discriminant has been refined by making the order-one coarse-graining factor Ξ\XiΞ explicit in the log-ratio. These changes improve internal consistency and derivational clarity while leaving the main physical conclusion unchanged: under a common EFT portal, the discriminating power between metric and Palatini formulations is carried by their different reheating histories and coarse-grained maps to (wreh,ΔNreh,Hend,σend)(w_{\rm reh}, \Delta N_{\rm reh}, H_{\rm end}, \sigma_{\rm end})(wreh,ΔNreh,Hend,σend).