FRW时空中的Dirac场：电流和能量动量
Dirac Field in FRW Spacetime: Current and Energy Momentum
摘要：
研究了FRW时空中Dirac场的行为。求解相关方程以确定粒子和能量分布。角向和径向部分用雅可比多项式求解。仅对充满辐射的平坦空间，用已知函数解出了质量场的时间依赖性。在一般的FRW空间中，采用WKB方法进行近似求解。在这两个独立的解中，一个被发现随着宇宙的膨胀而衰减，而另一个解则在增长。这可能是局部粒子流的来源。研究了粒子数和能量密度的变化规律。它被发现，粒子安排自己的数量和密度分布模式，产生一个恒定的牛顿势所需的星系的平坦的旋转曲线。此外，密度对比度被发现与膨胀的增长。
英文摘要：
The behaviour of the Dirac field in FRW space-time is investigated. The relevant equations are solved to determine the particle and energy distribution. The angular and radial parts are solved in terms of Jacobi polynomials. The time dependence of the massive field is solved in terms of known function only for the radiation filled flat space. WKB method is used for approximate solution in general FRW space. Of the two independent solutions, one is found to decay in time as the Universe expands, while the other solution grows. This could be the source of the local particle current. The behaviour of the particle number and energy density are also investigated. It is found that the particles arrange themselves in a number and density distribution pattern that produces a constant Newtonian potential as required for the flat rotation curves of galaxies. Further, density contrast is found to grow with the expansion.
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