论文标题
物理哈密顿量模拟重力
Physical Hamiltonian for mimetic gravity
论文作者
论文摘要
从模拟重力的局部动作开始，包括标量场$ ϕ $的较高衍生物，我们在ADM规范形式主义中在时间表$ ϕ = t $的情况下，在ADM规范形式主义中得出了量规固定的规范动作。这种降低的作用揭示了（i）一个非悬崖的保守物理哈密顿量，这是两个术语的总和，即对大麻的一般相对性约束的表达和扩展标量的函数，以及（ii）降低的符号结构，几何形式提供了dirac括号。作为我们的一般分析的应用，我们计算了物理哈密顿量和规范方程，以围绕Minkowski时空，同质宇宙学和球形对称的空间扰动。
Starting from a local action for mimetic gravity that includes higher derivatives of a scalar field $ϕ$, we derive a gauge-fixed canonical action of the theory in the ADM canonical formalism in the time gauge $ϕ=t$. This reduced action reveals (i) a non-vanishing conserved physical Hamiltonian that is a sum of two terms, the expression for the Hamiltonian constraint of general relativity and a function of the expansion scalar, and (ii) a reduced symplectic structure that geometrically provides the Dirac brackets. As applications of our general analysis, we compute the physical Hamiltonians and canonical equations for perturbations around Minkowski spacetime, homogeneous cosmologies, and spherically symmetric spacetimes.
