The Geometrical Origin of Dark Energy
  The geometrical formulation of the quantum Hamilton-Jacobi theory shows that
the quantum potential is never trivial, so that it plays the r\^ole 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 $$ \Lambda=-\frac{\kappa^2}{\sqrt{\bar g}}Q[g_{jk}] \ . $$ This
shows that the cosmological constant is a quantum correction of the Einstein
tensor, reminiscent of the von Weizs\"acker 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.
