There is marginal evidence that the quintessential form of matter responsible for the acceleration of the universe observed today has ratio between pressure and energy density w < -1 .
Such a regime , called superacceleration , can not be achieved with conventional scalar field models .
The simplest non-exotic model achieving superacceleration is that of a scalar field nonminimally coupled to the Ricci curvature .
This model is studied for general potentials and an exact superaccelerating solution is presented .
In quintessential inflation , the model can have blue gravitational wave spectra , improving the prospects for the detection of cosmological gravitational waves .