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arXiv 1409.6840astro-ph.CO
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来自额外维度的螺旋宇宙学磁场

Helical cosmological magnetic fields from extra-dimensions

Kumar Atmjeet, T. R. Seshadri, Kandaswamy Subramanian

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4 postscript figures, version submitted to Physical Review D
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摘要：

我们在电磁理论的高维推广下研究了螺旋宇宙磁场的暴胀产生。为此，我们还包括一个宇称破缺件的电磁作用。额外维的比例因子的演变允许打破共形不变性的有效电磁作用在$1+3$尺寸所需的这种生成。在某些特殊情况下，可以用库仑波函数得到矢量势的解析解。我们还提出了更一般情况下的矢势演化的数值解。在高维宇宙学常数存在的情况下，存在标度因子的解，其中正常和额外维空间以相同的速率同时膨胀或收缩。在这种情况下，与额外的维度$D=4$的数量，螺旋磁场的标度不变的频谱被获得。当一种螺旋模在超视界尺度上开始支配另一种螺旋模时，净螺旋度就产生了。对于暴胀尺度$H\simeq 10^{-3}$ $M_{pl}$，可以得到$10^{-9}$ $G$量级的磁场强度。较弱的磁场将在较低的暴胀尺度下产生。该模型中产生的磁场遵循普朗克和$γ$射线观测（即$10^{-16}$ $G$ $<$ $B_{obs}<3.4\times 10^{-9}$ $G$）对磁场的限制。

英文摘要：

We study the inflationary generation of helical cosmological magnetic fields in a higher-dimensional generalization of the electromagnetic theory. For this purpose, we also include a parity breaking piece to the electromagnetic action. The evolution of extra-dimensional scale factor allows the breaking of conformal invariance of the effective electromagnetic action in $1+3$ dimensions required for such generation. Analytical solutions for the vector potential can be obtained in terms of Coulomb wave-functions for some special cases. We also present numerical solutions for the vector potential evolution in more general cases. In the presence of a higher-dimensional cosmological constant there exist solutions for the scale factors in which both normal and extra dimensional space either inflate or deflate simultaneously with the same rate. In such a scenario, with the number of extra dimensions $D=4$, a scale invariant spectrum of helical magnetic field is obtained. The net helicity arises, as one helical mode comes to dominate over the other at the superhorizon scales. A magnetic field strength of the order of $10^{-9}$ $G$ can be obtained for the inflationary scale $H\simeq 10^{-3}$ $M_{pl}$. Weaker fields will be generated for lower scales of inflation. Magnetic fields generated in this model respects the bounds on magnetic fields by Planck and $γ$-ray observations (i.e. $10^{-16}$ $G$ $<$ $B_{obs}<3.4\times 10^{-9}$ $G$).

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