De Sitter ground state of scalar-tensor gravity and its fluctuation with
  dust
  An exact de Sitter solution of scalar-tensor gravity is found, in which the
non-minimal coupling scalar is rolling along a non-constant potential. Based on
this solution, a dust-filled FRW universe is explored in frame of scalar-tensor
gravity. The effective dark energy induced by the sole non-minimal scalar can
be quintessence-like, phantom-like, and more significantly, can cross the
phantom divide. The rich and varied properties of scalar-tensor gravity even
with only one scalar is shown in this article.
