  We find that the expansion of the universe is accelerating by analyzing the
recent observation data of type $\textsc{I}a$ supernova(SN-Ia) .It indicates
that the equation of state of the dark energy might be smaller than -1,which
leads to the introduction of phantom models featured by its negative kinetic
energy to account for the regime of equation of state parameter $w<-1$.In this
paper the possibility of using a non-minimally coupled real scalar field as
phantom to realize the equation of state parameter $w<-1$ is discussed.The main
equations which govern the evolution of the universe are obtained.Then we
rewrite them with the observable quantities.

General Relativity and Quantum Cosmology