We investigate the generation of magnetic fields from inflation, which occurs via breakdown of the conformal invariance of the electromagnetic (EM) field, when coupled with the Ricci scalar and the Gauss-Bonnet invariant. For the case of instantaneous reheating, the resulting strength of the magnetic field at present is too small and violates the observational constraints. However, the problem is solved provided there is a reheating phase with a non-zero e-fold number. During reheating, the energy density of the magnetic field is seen to evolve as (a ³ H)^-2 and, after that, as a ^-4 up to the present epoch (here a is the scale factor and H the Hubble parameter). It is found that this reheating phase –characterized by a certain e-fold number, a constant value of the equation of state parameter, and a given reheating temperature– renders the magnetogenesis model compatible with the observational constraints. The model provides, in turn, a viable way of constraining the reheating equation of state parameter, from data analysis of the cosmic microwave background radiation.

我们研究了膨胀产生的磁场，膨胀是通过破坏电磁 (EM) 场的共形不变性与 Ricci 标量和 Gauss-Bonnet 不变量相结合而发生的。对于瞬时再加热的情况，目前产生的磁场强度太小，违反了观测约束。但是，如果存在具有非零 e 折叠数的再加热阶段，问题就解决了。在再加热期间，磁场的能量密度被视为演变为 ( a ³ H ) ^-2，然后，直到当前时期，磁场的能量密度演变为 ^-4（这里 a 是比例因子，H哈勃参数）。发现这个再加热阶段——以特定的 e 倍数、状态方程参数的恒定值和给定的再加热温度为特征——使磁发生模型与观测约束兼容。反过来，该模型通过对宇宙微波背景辐射的数据分析，提供了一种约束状态参数再加热方程的可行方法。