arXiv 1105.44202011-05gr-qc

多维宇宙学中的向量场

Vector fields in multidimensional cosmology

Boris E. Meierovich

备注：: The journal reference of this article: PHYSICAL REVIEW D 84, 064037 (2011) This updated version reflects the recommendations of the referees, contains additional references and figures of better quality
发表信息：: Physical Review D 84, 064037 (2011)
DOI：: 10.1103/PhysRevD.84.064037

摘要：

膨胀宇宙中的矢量场被认为是广义相对论的多维理论。广义相对论中的向量场形成一个三参数簇。我们的考虑包括非零协变散度的领域。根据特定参数与问题对称性之间的关系，矢量场可以是纵向的和/或横向的，也可以是超相对论性的（即无质量）或非相对论性的（有质量），等等。在大多数情况下，场方程简化为贝塞尔方程，并分析了它们的时间演化。最简单的零质量纵向矢量场的能量-动量张量作为宇宙学常数的附加项进入爱因斯坦方程。在这种情况下，德西特度规是爱因斯坦方程的精确解。因此，最简单的零质量纵向矢量场假装是宏观描述暗能量作为宇宙以恒定速率膨胀的来源的适当工具。零质量矢量场在膨胀过程中不为零。相反，大规模的场会随着时间而消失。虽然它们的振幅在下降，但巨大的磁场使膨胀加速。宇宙学中向量场的宏观分析放弃了在爱因斯坦的广义相对论中解决主要难题--单个物体之间的吸引力和整个宇宙的膨胀--的希望。

英文摘要：

Vector fields in the expanding Universe are considered within the multidimensional theory of General Relativity. Vector fields in general relativity form a three-parametric variety. Our consideration includes the fields with a nonzero covariant divergence. Depending on the relations between the particular parameters and the symmetry of a problem, the vector fields can be longitudinal and/or transverse, ultrarelativistic (i.e. massless) or nonrelativistic (massive), and so on. The longitudinal and transverse vector fields are considered separately in detail in the background of the de Sitter cosmological metric. In most cases the field equations reduce to Bessel equations, and their temporal evolution is analyzed analytically. The energy-momentum tensor of the most simple zero-mass longitudinal vector fields enters the Einstein equations as an additive to the cosmological constant. In this case the de Sitter metric is the exact solution of the Einstein equations. Hence, the most simple zero-mass longitudinal vector field pretends to be an adequate tool for macroscopic description of dark energy as a source of the expansion of the Universe at a constant rate. The zero-mass vector field does not vanish in the process of expansion. On the contrary, massive fields vanish with time. Though their amplitude is falling down, the massive fields make the expansion accelerated. The macroscopic analysis of vector fields in cosmology gives up the hope that the major puzzle -- attraction between individual objects and expansion of the Universe as a whole -- can be solved within the Einstein's theory of general relativity.

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