Effect of matter structure on the gravitational waveform

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 time of coalescence made by LISA will have an impact on the prediction of the time at which the signal will be visible by ground based interferometers, for signals spanning both frequency bands.