Quadrupolar power radiation by a binary system in a hyperbolic encounter on de Sitter background

Abstract: The present cosmological model and the surveys favor the universe with a small but positive cosmological constant $\Lambda$, which accounts for dark energy and causes an exponential expansion. This can have observational consequences in the current detection of gravitational waves, as most of the waveforms for gravitational radiation are computed assuming a flat (Minkowski) background. In this work, we compute gravitational radiation within the quadrupole approximation on positive $\Lambda$ (de Sitter) background for a binary system interacting gravitationally through a hyperbolic encounter. We quantify the influence of the cosmological constant on the radiated energy as small corrections to the leading order Minkowski background results. The first order de Sitter background correction is of the order $\sqrt{\Lambda}$, and is thus extremely small. Therefore, the cosmological constant influence on the gravitational radiation is negligible and may not be detected with the existing or planned gravitational wave detectors.