论文标题
曲率扰动$ζ$
A (semi)-exact Hamiltonian for the curvature perturbation $ζ$
论文作者
论文摘要
一般相对论中的哈密顿量总数涉及一流的哈密顿量和动量限制，却消失了。但是，当动作围绕经典解决方案扩展（例如单个标量场膨胀模型）时，似乎没有逐渐变化的哈密顿量和其他一流的约束。但是这一次，理论在波动场的数量中变得扰动。我们表明，可以重新组织这种扩展并准确地解决哈密顿的约束，从而产生明确的所有订单动作。另一方面，动量约束可以通过保持曲率扰动$ζ$依赖性确切的张力模式$γ_{ij} $进行扰动。通过这种方式，在量规修复后，可以以$ζ$获得半脱光度的哈密顿量，该$ζ$只能从与张量模式的交互中进行校正（因此，当张量扰动设置为零时，汉密尔顿人变得精确了）。当$ζ$的演变涉及对数时间依赖性时，运动方程清楚地表现出来，这是文献中争论的微妙点。我们讨论了长波长和较晚的时间限制，并获得了$ζ$零模式的一些简单但非平凡的经典解决方案。
The total Hamiltonian in general relativity, which involves the first class Hamiltonian and momentum constraints, weakly vanishes. However, when the action is expanded around a classical solution as in the case of a single scalar field inflationary model, there appears a non-vanishing Hamiltonian and additional first class constraints; but this time the theory becomes perturbative in the number of fluctuation fields. We show that one can reorganize this expansion and solve the Hamiltonian constraint exactly, which yield an explicit all order action. On the other hand, the momentum constraint can be solved perturbatively in the tensor modes $γ_{ij}$ by still keeping the curvature perturbation $ζ$ dependence exact. In this way, after gauge fixing, one can obtain a semi-exact Hamiltonian for $ζ$ which only gets corrections from the interactions with the tensor modes (hence the Hamiltonian becomes exact when the tensor perturbations set to zero). The equations of motion clearly exhibit when the evolution of $ζ$ involves a logarithmic time dependence, which is a subtle point that has been debated in the literature. We discuss the long wavelength and late time limits, and obtain some simple but non-trivial classical solutions of the $ζ$ zero-mode.
