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Unveiling the origin of the coalescing binaries detected via gravitational waves (GW) is challenging, notably if no multi-wavelength counterpart is detected. One important diagnostic tool is the coalescing binary distribution with respect to the large scale structures (LSS) of the universe, which we quantify via the cross-correlation of galaxy catalogs with GW ones. By using both existing and forthcoming galaxy catalogs and using realistic Monte Carlo simulations of GW events, we find that the cross-correlation signal should be marginally detectable in a 10-year data taking of advanced LIGO-Virgo detectors at design sensitivity, at least for binary neutron star mergers. The expected addition of KAGRA and LIGO-India to the GW detector network would allow for a firmer detection of this signal and, in combination with future cosmological surveys, would also permit the detection of cross-correlation for coalescing black holes. Such a measurement may unveil, for instance, a primordial origin of coalescing black holes. To attain this goal, we find that it is crucial to adopt a tomographic approach and to reach a sufficiently accurate localization of GW events. The depth of forthcoming surveys will be fully exploited by third generation GW detectors such as the Einstein Telescope or the Cosmic Explorer, which will allow one to perform precision studies of the coalescing black hole LSS distribution and attain rather advanced model discrimination capabilities., Comment: 14 pages, 11 multi-panel figures. v2: Improved discussion and presentation, results and conclusions unchanged; closely matches published version

We assume that the cosmological dark matter is composed of massive neutral scalar particles that decay into two massless particles. The decay produces a stochastic background of gravitational waves (GWs) via a 'memory effect' mechanism. We calculate the spectral amplitude and slope of the resulting background, which is frequency independent (flat). We discuss its potential observability and show that the resulting background might dominate the cosmological GW background at frequencies above about 10 GHz. Penrose has proposed a cosmological model in which dark matter particles have the Planck mass and decay into two gravitons. For these, the spectrum has an additional 'direct' contribution from the decay products, which we also calculate. At low frequencies, this direct contribution also has a flat spectrum but with a much smaller amplitude than the memory part., Comment: Final published version (Open Access)

We present a novel numerical routine (oscode) with a C++ and Python interface for the efficient solution of one-dimensional, second-order, ordinary differential equations with rapidly oscillating solutions. The method is based on a Runge-Kutta-like stepping procedure that makes use of the Wentzel-Kramers-Brillouin (WKB) approximation to skip regions of integration where the characteristic frequency varies slowly. In regions where this is not the case, the method is able to switch to a made-to-measure Runge-Kutta integrator that minimises the total number of function evaluations. We demonstrate the effectiveness of the method with example solutions of the Airy equation and an equation exhibiting a burst of oscillations, discussing the error properties of the method in detail. We then show the method applied to physical systems. First, the one-dimensional, time-independent Schr\"odinger equation is solved as part of a shooting method to search for the energy eigenvalues for a potential with quartic anharmonicity. Then, the method is used to solve the Mukhanov-Sasaki equation describing the evolution of cosmological perturbations, and the primordial power spectrum of the perturbations is computed in different cosmological scenarios. We compare the performance of our solver in calculating a primordial power spectrum of scalar perturbations to that of BINGO, an efficient code specifically designed for such applications., Comment: Physical Review Research, accepted. 23 pages, 15 figures. The associated code is available online at https://github.com/fruzsinaagocs/oscode