Inflationary Magnetogenesis with f(R,ϕ) Coupling
Abstract
Inflationary magnetogenesis provides a promising mechanism for generating primordial large-scale magnetic fields, but faces challenges such as the strong coupling problem and backreaction issues. In this paper, we extend the Ratra model by introducing a coupling between the electromagnetic field and the background geometry, parameterized as K(R)I2(ϕ). Starting from a general action with f2(R,ϕ)FμνFμν, we adopt f2(R,ϕ)=K(R)I2(ϕ) as a concrete realization. Rather than focusing on the slow-roll inflationary stage (which reduces to the standard Ratra scenario), we concentrate on the post-inflationary reheating epoch, where the broken-power-law evolution of the scale factor and coupling function across the inflation-to-reheating transition allows us to derive analytic expressions for the magnetic and electric energy density spectra. Three key theoretical constraints are imposed on the model parameter space: the strong coupling condition, the backreaction constraint, and the CMB isotropy requirement. We obtain predictions for the present-day magnetic field strength B0 and coherence length Lc0 for various combinations of the inflationary energy scale Hf and the reheating temperature Tr. By comparing with observational constraints from radio observations and Fermi-LAT gamma-ray data, we demonstrate that the inflationary energy scale Hf, the reheating temperature Tr, the parameter β, and the e-folding numbers Nf, Nr must satisfy stringent joint constraints. This work provides a viable theoretical framework for inflationary magnetogenesis that simultaneously satisfies theoretical consistency conditions and current observational bounds, with the reheating-stage nonlinear MHD evolution serving as a crucial ingredient for producing observationally compatible magnetic fields.
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BibTeX
@misc{liu2026inflationary,
title = {{Inflationary Magnetogenesis with $f(R,ϕ)$ Coupling}},
author = {Shuang Liu and Bo-yu Zhao and Yu Li and Yao-chuan Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01977},
eprint = {2609.01977},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01977},
}
RIS
TY - UNPB
TI - Inflationary Magnetogenesis with f(R,ϕ) Coupling
AU - Shuang Liu
AU - Bo-yu Zhao
AU - Yu Li
AU - Yao-chuan Wang
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.01977
UR - https://arxiv.org/abs/2609.01977
AB - Inflationary magnetogenesis provides a promising mechanism for generating primordial large-scale magnetic fields, but faces challenges such as the strong coupling problem and backreaction issues. In this paper, we extend the Ratra model by introducing a coupling between the electromagnetic field and the background geometry, parameterized as K(R)I^2(ϕ). Starting from a general action with f^2(R,ϕ)F_μνF^μν, we adopt f^2(R,ϕ)=K(R)I^2(ϕ) as a concrete realization. Rather than focusing on the slow-roll inflationary stage (which reduces to the standard Ratra scenario), we concentrate on the post-inflationary reheating epoch, where the broken-power-law evolution of the scale factor and coupling function across the inflation-to-reheating transition allows us to derive analytic expressions for the magnetic and electric energy density spectra. Three key theoretical constraints are imposed on the model parameter space: the strong coupling condition, the backreaction constraint, and the CMB isotropy requirement. We obtain predictions for the present-day magnetic field strength B_0 and coherence length L_c0 for various combinations of the inflationary energy scale H_f and the reheating temperature T_r. By comparing with observational constraints from radio observations and Fermi-LAT gamma-ray data, we demonstrate that the inflationary energy scale H_f, the reheating temperature T_r, the parameter β, and the e-folding numbers N_f, N_r must satisfy stringent joint constraints. This work provides a viable theoretical framework for inflationary magnetogenesis that simultaneously satisfies theoretical consistency conditions and current observational bounds, with the reheating-stage nonlinear MHD evolution serving as a crucial ingredient for producing observationally compatible magnetic fields.
ER -