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The existence of primordial black holes (PBHs), which may form from the collapse of matter overdensities shortly after the Big Bang, is still under debate. Among the potential signatures of PBHs are gravitational waves (GWs) emitted from binary black hole (BBH) mergers at redshiftsz≳ 30, where the formation of astrophysical black holes is unlikely. Future ground-based GW detectors, the Cosmic Explorer and Einstein Telescope, will be able to observe equal-mass BBH mergers with total mass of$\mathit{}(10–100)M_{\odot }$at such distances. In this work, we investigate whether the redshift measurement of a single BBH source can be precise enough to establish its primordial origin. We simulate BBHs of different masses, mass ratios and orbital orientations. We show that for BBHs with total masses between 20M_⊙and 40M_⊙merging atz≥ 40, one can inferz> 30 at up to 97% credibility, with a network of one Einstein Telescope, one 40 km Cosmic Explorer in the US, and one 20 km Cosmic Explorer in Australia. This number reduces to 94% with a smaller network made of one Einstein Telescope and one 40 km Cosmic Explorer in the US. We also analyze how the measurement depends on the Bayesian priors used in the analysis and verify that priors that strongly favor the wrong model yield smaller Bayesian evidences.

The Einstein Telescope (ET), the European project for a third-generation gravitational-wave detector, has a reference configuration based on a triangular shape consisting of three nested detectors with 10 km arms, where each detector has a 'xylophone' configuration made of an interferometer tuned toward high frequencies, and an interferometer tuned toward low frequencies and working at cryogenic temperature. Here, we examine the scientific perspectives under possible variations of this reference design. We perform a detailed evaluation of the science case for a single triangular geometry observatory, and we compare it with the results obtained for a network of two L-shaped detectors (either parallel or misaligned) located in Europe, considering different choices of arm-length for both the triangle and the 2L geometries. We also study how the science output changes in the absence of the low-frequency instrument, both for the triangle and the 2L configurations. We examine a broad class of simple 'metrics' that quantify the science output, related to compact binary coalescences, multi-messenger astronomy and stochastic backgrounds, and we then examine the impact of different detector designs on a more specific set of scientific objectives.

Gravity fluctuations produced by ambient seismic fields are predicted to limit the sensitivity of the next generation, gravitational wave detector Einstein Telescope at frequencies below 20 Hz. The detector will be hosted in an underground infrastructure to reduce seismic disturbances and associated gravity fluctuations. Additional mitigation might be required by monitoring the seismic field and using the data to estimate the associated gravity fluctuations and to subtract the estimate from the detector data, a technique called coherent noise cancelation. In this paper, we present a calculation of correlations between surface displacement of a seismic field and the associated gravitational fluctuations using the spectral element SPECFEM3D Cartesian software. The model takes into account the local topography at a candidate site of the Einstein Telescope at Sardinia. This paper is a first demonstration of SPECFEM3D's capabilities to provide estimates of gravitoelastic correlations, which are required for an optimized deployment of seismometers for gravity noise cancelation.