论文标题
暗能量的几何起源
The Geometrical Origin of Dark Energy
论文作者
论文摘要
量子汉密尔顿 - 雅各比理论的几何表述表明,量子电位从来都不是微不足道的,因此它播放了内在能量的ro方。这样的关键属性选择了Wheeler-Dewitt(WDW)量子电位$ Q [G_ {JK}] $作为黑暗能源的自然候选人。这导致具有消失的动力学术语的WDW Hamilton-Jacobi方程,并带有标识$$λ= - \ frac {κ^2} {\ sqrt {\ bar g}} q [g_ {jk}] \。 $$这表明宇宙常数是爱因斯坦张量的量子校正,让人联想到vonWeizsäcker校正到托马斯 - 费尔米理论的动力学项。量子电位还定义了Madelung压力张量。真空能量密度的几何起源是一种严格的非扰动现象,提供了有力的证据,表明它是由于重力凝结物所致。正则化WDW方程的时间独立性表明,普朗克长度与哈勃半径之间的比率可能是一个时间常数,提供红外/紫外线二元性。我们推测,这种双重性与恒定曲率的局部到全局几何定理有关,表明了解宇宙几何形状对于量子重力的表述至关重要。
The geometrical formulation of the quantum Hamilton-Jacobi theory shows that the quantum potential is never trivial, so that it plays the rôle of intrinsic energy. Such a key property selects the Wheeler-DeWitt (WDW) quantum potential $Q[g_{jk}]$ as the natural candidate for the dark energy. This leads to the WDW Hamilton-Jacobi equation with a vanishing kinetic term, and with the identification $$ Λ=-\frac{κ^2}{\sqrt{\bar g}}Q[g_{jk}] \ . $$ This shows that the cosmological constant is a quantum correction of the Einstein tensor, reminiscent of the von Weizsäcker correction to the kinetic term of the Thomas-Fermi theory. The quantum potential also defines the Madelung pressure tensor. The geometrical origin of the vacuum energy density, a strictly non-perturbative phenomenon, provides strong evidence that it is due to a graviton condensate. Time independence of the regularized WDW equation suggests that the ratio between the Planck length and the Hubble radius may be a time constant, providing an infrared/ultraviolet duality. We speculate that such a duality is related to the local to global geometry theorems for constant curvatures, showing that understanding the universe geometry is crucial for a formulation of Quantum Gravity.