  Third generation ground-based interferometers as well as the planned
space-based interferometer LISA are expected to detect a plethora of
gravitational wave signals from coalescing binaries at cosmological distance.
The emitted gravitational waves propagate in the expanding universe through the
inhomogeneous distribution of matter. Here we show that the acceleration of the
universe and the peculiar acceleration of the binary with respect to the
observer distort the gravitational chirp signal from the simplest General
Relativity prediction beyond a mere time independent rescaling of the chirp
mass, affecting intrinsic parameter estimations for the binaries visible by
LISA. We find that the effect due to the peculiar acceleration can be much
larger than the one due to the universe acceleration. Moreover, peculiar
accelerations can introduce a bias in the estimation of parameters such as the
time of coalescence and the individual masses of the binary. An error in the
estimation of the arrival time will have an impact in the case of sources
visible first by LISA and later by ground based interferometers.
