Title: Primordial Magnetic Helicity from Stochastic Electric Currents Show Chinese title

Title: 原始磁螺旋度来自随机电流

Abstract: We study the possibility that primordial magnetic fields generated in the transition between inflation and reheating posses magnetic helicity, $H_M$. The fields are induced by stochastic currents of scalar charged particles created during the mentioned transition. We estimate the rms value of the induced magnetic helicity by computing different four-point SQED Feynman diagrams. For any considered volume, the magnetic flux across its boundaries is in principle non null, which means that the magnetic helicity in those regions is gauge dependent. We use the prescription given by Berger and Field and interpret our result as the difference between two magnetic configurations that coincide in the exterior volume. In this case the magnetic helicity gives only the number of magnetic links inside the considered volume. We calculate a concrete value of $H_M$ for large scales and analyze the distribution of magnetic defects as a function of the scale. Those defects correspond to regular as well as random fields in the considered volume. We find that the fractal dimension of the distribution of topological defects is $D = 1/2$. We also study if the regular fields induced on large scales are helical, finding that they are and that the associated number of magnetic defects is independent of the scale. In this case the fractal dimension is $D=0$. We finally estimate the intensity of fields induced at the horizon scale of reheating, and evolve them until the decoupling of matter and radiation under the hypothesis of inverse cascade of magnetic helicity. The resulting intensity is high enough and the coherence length long enough to have an impact on the subsequent process of structure formation. Show Chinese abstract

Abstract: 我们研究在暴胀和再加热过渡期间产生的原初磁场是否具有磁螺旋性，$H_M$。 这些磁场是由在上述过渡期间产生的标量带电粒子的随机电流引起的。 我们通过计算不同的四点SQED费曼图来估计感应磁螺旋性的均方根值。 对于任何考虑的体积，其边界的磁通量原则上是非零的，这意味着这些区域的磁螺旋性是规范依赖的。 我们使用Berger和Field提供的方法，并将我们的结果解释为两个在外部体积中一致的磁配置之间的差异。 在这种情况下，磁螺旋性仅给出所考虑体积内的磁链接数量。 我们计算了大尺度上的$H_M$的具体值，并分析了磁缺陷分布随尺度的变化。 这些缺陷对应于所考虑体积中的规则场和随机场。 我们发现拓扑缺陷分布的分形维数为$D = 1/2$。 我们还研究了在大尺度上诱导的规则场是否具有螺旋性，发现它们确实具有螺旋性，并且相关的磁缺陷数量与尺度无关。 在这种情况下，分形维数为$D=0$。 我们最终估计了在再加热视界尺度上诱导的磁场强度，并在磁螺旋性逆级联假设下，将它们演化到物质和辐射分离时期。 结果表明，磁场强度足够高，相干长度足够长，足以对后续的结构形成过程产生影响。