发表机构
School of Science, Dalian Maritime University（大连海事大学理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文将Ratra模型扩展为非最小f(R)引力框架，推导reheating阶段磁场能谱，施加三类理论约束并结合MHD湍流效应，通过数值计算得到参数联合约束，为暴胀磁生成提供了可行理论框架。
AI 中文摘要
暴胀磁生成为原初大尺度磁场的产生提供了一种有前景的机制，但面临诸多挑战。本文将Ratra模型扩展为非最小f(R)引力框架，该框架在拉格朗日中以$f^2(\tau) F_{\mu\nu}F^{\mu\nu}$的形式出现，用于打破标准电磁作用的共形不变性。聚焦于暴胀后reheating阶段，我们通过构造暴胀到reheating过渡期间尺度因子和耦合函数的破幂律演化，推导了磁场和电场能谱的解析表达式。对模型参数空间施加三个关键理论约束：强耦合条件、反作用约束和CMB各向同性要求。通过数值计算，我们针对不同的暴胀能标$H_f$和reheating温度$T_r$组合，得到了现今磁场强度$B_0$和相干长度$L_{c0}$的预测。我们进一步纳入reheating后磁流体动力学（MHD）湍流的非线性效应，包括逆转移过程，这显著提升了相干长度（可达0.1 Mpc），同时使场强度降低数个数量级。通过与射电观测及Fermi-LAT伽马射线数据的观测约束对比，我们证明暴胀能标$H_f$、reheating温度$T_r$、参数$\beta$及e折叠数$N_f$、$N_r$必须满足严格的联合约束。本工作为暴胀磁生成提供了一种可行的理论框架，其同时满足理论一致性条件和当前观测界限。
英文摘要
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 $f^2(R,ϕ)F_{μν}F^{μν}$, 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.
Comments19 pages, 8 figures
