  Future generation of interferometric gravitational wave detectors is hoped to
provide accurate measurements of the final stages of binary inspirals. The
sources probed by such experiments are of extragalactic origin and the observed
chirp mass is the intrinsic chirp mass multiplied by $(1+z)$ where $z$ is the
redshift of the source. Moreover the luminosity distance is a direct observable
is such experiments. This creates the possibility to establish a new kind of
cosmological tests, supplementary to more standard ones.
  Recent observations of distant type Ia supernovae light-curves suggest that
the expansion of the universe has recently begun to accelerate. A popular
explanation of present accelerating expansion of the universe is to assume that
some part $\Omega_Q$ of the matter-energy density is in the form of dark
component called ``the quintessence'' with the equation of state $p_Q = w
\rho_Q$ with $w \geq -1.$ In this paper we consider the predictions concerning
observations of binary inspirals in future LIGO type interferometric
experiments assuming a ``quintessence cosmology''. In particular we compute the
expected redshift distributions of observed events in the a priori admissible
range of parameters describing the equation of state for the quintessence. We
find that this distribution has a robust dependence on the cosmic equation of
state.
