Science with the Einstein Telescope: a Comparison of Different Designs

The Einstein Telescope (ET), the European project for a third-generation gravitational-wave detector, has a reference configuration based on a triangular shape con-sisting 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 interferome-ter 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.