  A gravity theory is developed with the metric ${\hat g}_{\mu\nu}=
{g}_{\mu\nu}+B\partial_\mu\phi\partial_\nu\phi$. In the present universe the
additional contribution from the scalar field in the metric ${\hat g}_{\mu\nu}$
can generate an acceleration in the expansion of the universe, without negative
pressure and with a zero cosmological constant. In this theory, gravitational
waves will propagate at a different speed from non-gravitational waves. It is
suggested that gravitational wave experiments could test this observational
signature.
