哈密顿宇宙学
Hamiltonian Cosmology
摘要：
从哈密顿的角度研究了平空间Robertson-Walker几何的宇宙标度因子$a(t)$，其中$a(t)$被解释为一个独立的动力学坐标，曲率密度$\sqrt {- g(a)} R({a,\dot a,\ddot a})$被看作是闵可夫斯基时空中的作用量密度.正如所料，由此产生的$a(t)$的汉密尔顿只是传统方法（即广义相对论的罗伯逊-沃克宇宙学）的第一个弗里德曼方程。然而，这种方法的实用性源于这样一个事实，即物质、辐射和真空中的每一项，包括动力学/引力场项，在形式上都是能量密度，并且方程作为一个整体成为能量守恒的形式陈述。这种方法的一个优点是，它有助于直观地理解能量平衡和交换的宇宙尺度，否则在传统的介绍。每个坐标系都有自己内部一致的解释如何实现能量平衡。例如，在具有线元$ds^2 = dt^2 - a^2(t) d{\bf{x}}^2$的时空中，宇宙学红移是由于标量场$a(t)$和电磁场之间的后复合相互作用而出现的，其中电磁场释放能量，就好像通过均匀的有耗介质传播一样，而能量损失到尺度因子有助于驱动宇宙学膨胀。
英文摘要：
The cosmological scale factor $a(t)$ of the flat-space Robertson-Walker geometry is examined from a Hamiltonian perspective wherein $a(t)$ is interpreted as an independent dynamical coordinate and the curvature density $\sqrt {- g(a)} R({a,\dot a,\ddot a})$ is regarded as an action density in Minkowski spacetime. The resulting Hamiltonian for $a(t)$ is just the first Friedmann equation of the traditional approach (i.e. the Robertson-Walker cosmology of General Relativity), as might be expected. The utility of this approach however stems from the fact that each of the terms matter, radiation, and vacuum, and including the kinetic / gravitational field term, are formally energy densities, and the equation as a whole becomes a formal statement of energy conservation. An advantage of this approach is that it facilitates an intuitive understanding of energy balance and exchange on the cosmological scale that is otherwise absent in the traditional presentation. Each coordinate system has its own internally consistent explanation for how energy balance is achieved. For example, in the spacetime with line element $ds^2 = dt^2 - a^2(t) d{\bf{x}}^2$, cosmological red-shift emerges as due to a post-recombination interaction between the scalar field $a(t)$ and the EM fields in which the latter loose energy as if propagating through a homogeneous lossy medium, with the energy lost to the scale factor helping drive the cosmological expansion.
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