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, affecting parameter estimations for the binaries visible by LISA. We find that the effect due to peculiar acceleration can be much larger than the one due to the universe acceleration, thereby excluding the possibility of using this latter to infer the redshift of the GW source (as previously proposed). 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.